MathIsPower4U / High School / Math
Lecture : Volume of Revolution - The Washer Method about the x-axis
By James Sousa | Fundamentals of Calculus
Lecture 87 of 314
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 More Lectures - Select Lecture...1 : Introduction to Limits2 : Determining Limits3 : Limits At Infinity4 : Limits At Infinity - Additional Examples5 : Determining Limits of Trigonometric Functions6 : The Squeeze Theorem and Special Limits7 : Determining Limits Using Special Limits8 : Continuity using Limits9 : Horizontal Vertical Asymptotes - Part 1 of 210 : Horizontal Vertical Asymptotes - Part 2 of 211 : Average Rate of Change12 : Introduction to the Derivative13 : Finding Derivatives Using the Limit Defintion14 : Differentiation Techniques: Power Rule15 : The Derivative of Sine and Cosine16 : How to Determine the Value of a Derivative Function on the Graphing Calculator.17 : Applications of the Derivative: The Power Rule18 : The Product Rule19 : The Quotient Rule20 : The Product and Quotient Rule With Trigonometric Functions21 : Elasticity of Demand - Part 1 of 222 : Elasticity of Demand - Part 2 of 223 : Average Revenue, Cost, and Profit Functions and Their Derivatives24 : The Chain Rule: Part 1 of 225 : The Chain Rule: Part 2 of 226 : The Chain Rule With Transcendental Functions27 : Higher-Order Derivatives: Part 1 of 228 : Higher-Order Derivatives: Part 2 of 229 : Higher Order Derivatives of Trigonometric Functions30 : Determining where a function is increasing and decreasing using the first deriviative31 : Increasing and Decreasing Trig Functions Relative Extrema32 : Finding relative extrema using the first derivative33 : How to Determine Relative Extrema on the Graphing Calculator34 : Max and Min Apps. w Calculus - Part 1 of 235 : Max and Min Apps. w Calculus - Part 2 of 236 : Determining the concavity of a function37 : Concavity - Additional Examples38 : The second derivative test to determine relative extrema39 : The Second Derivative Test - Additional Examples with Transcendental Functions40 : Summary of the First and Second Derivative of a Function41 : Animation: The graph of a function and its 1st and 2nd Derivative42 : Marginals43 : Absolute Extrema44 : Absolute Extrema of Transcendental Functions45 : Rolles Theorem46 : The Mean Value Theorem47 : Implicit Differentiation48 : Implicit Differentiation with Transcendental Functions49 : Related Rates50 : Newtons Method51 : Graph Exponential Functions52 : Derivatives of Exponential Functions with Base e53 : Logarithms54 : Derivative of the Logarithmic Function55 : The Derivatives of Exponential and Logarithmic Functions (Base not equal to e)56 : Logarithmic Differentiation57 : The Derivatives of Inverse Trigonometric Functions58 : Sigma Notation59 : Area Under A Graph60 : The Antiderivative61 : The Six Basic Trigonometric Integration Formulas62 : Examples Part 1: Integrate using the Six Basic Trig Integral Formulas63 : Examples Part 2: Integrate using the Six Basic Trig Integral Formulas64 : The Definite Integral65 : Determine the Value of a Definite Integral on the Graphing Calculator66 : Average Value67 : Equilibrium Point68 : Consumer and Producer Surplus69 : Future and Present Value - Part 1 of 270 : Future and Present Value - Part 2 of 271 : The Area Between Two Graphs72 : Integration Using Substitution - Part 1 of 273 : Integration Using Substitution - Part 2 of 274 : Integration by Parts: The Basics75 : Integration by Parts76 : Integration by Parts - Additional Examples77 : The Trapezoid Rule78 : Simpsons Rule79 : Integration Involving Inverse Trig Functions - Part 180 : Integration Involving Inverse Trig Functions: Part 281 : Integration Involving Inverse Trig Functions: Part 382 : Improper Integrals83 : Introduction to Differential Equations84 : Differential Equations and the Exponential Function85 : Solving Differential Equations by Separation of Variables86 : Volume of Revolution - The Disk Method87 : Volume of Revolution - The Washer Method about the x-axis88 : Volume of Revolution - The Washer Method about the y-axis89 : Volume of Revolution - The Washer Method NOT about the x or y axis90 : Volume of Revolution - The Shell Method about the x-axis91 : Volume of Revolution - The Shell Method about the y-axis92 : Volume of Revolution - The Shell Method NOT about x or y axis93 : Volume of Revolution - Comparing the Washer and Shell Method94 : Arc Length - Part 1 of 295 : Arc Length - Part 2 of 296 : Surface Area of Revolution - Part 1 of 297 : Surface Area of Revolution - Part 2 of 2 (about y-axis)98 : Trigonometric Integrals Involving Powers of Sine and Cosine - Part 199 : Trigonometric Integrals Involving Powers of Sine and Cosine - Part 2100 : Trigonometric Integrals Involving Powers of Secant and Tangent - Part 1101 : Trigonometric Integrals Involving Powers of Secant and Tangent - Part 2102 : Partial Fraction Decomposition - Part 1 of 2103 : Partial Fraction Decomposition - Part 2 of 2104 : Integration Using Partial Fraction Decomposition Part 1105 : Integration Using Partial Fraction Decomposition Part 2106 : Integration Involving Trigonometric Substitution Part 1107 : Integration Involving Trigonometric Substitution Part 2108 : Integration Involving Trigonometric Substitution Part 3109 : Integration Involving Trigonometric Substitution Part 4110 : Walliss Formula to Integrate Powers of Sine or Sine 0, pi-2111 : L Hopitals Rule Part 1112 : L Hopitals Rule Part 2113 : Introduction to Sequences114 : Arithmetic Sequences115 : Geometric Sequences116 : Sequences on the TI84 Graphing Calculator117 : Limits of a Sequence118 : Limits of a Sequence: The Squeeze Theorem119 : Arithmetic Series120 : Geometric Series121 : Introduction to Infinite Series122 : Infinite Geometric Series123 : Sequences and Series on the TI83-84 Graphing Calculator124 : Graphing Partial Sums of an Infinite Series on the TI84125 : Telescoping Series126 : The Integral Test127 : The p-Series Test128 : The Comparison Test129 : The Limit Comparison Test130 : The Root Test131 : The Ratio Test132 : The Alternating Series Test133 : Absolutely and Conditionally Convergent Series134 : Using Taylor Polynomials to Approximate Functions135 : Taylors Theorem with Remainder136 : Power Series - Part 1137 : Power Series - Part 2138 : Representing a Function as a Geometric Power Series - Part 1139 : Representing a Function as a Geometric Power Series - Part 2140 : Taylor and Maclaurin Series141 : Using a Table of Basic Power Series to Determine More Power Series - Part 1142 : Using a Table of Basic Power Series to Determine More Power Series - Part 2143 : Differentiation and Integration Using Power Series144 : Introduction to Parametric Equations145 : Graphing Parametric Equations on the TI84146 : Converting Parametric Equation to Rectangular Form147 : The Derivative of Parametric Equations148 : The Second Derivative of Parametric Equations - Part 1 of 2149 : The Second Derivative of Parametric Equations - Part 2 of 2150 : Arc Length Using Parametric Equations151 : Surface Area of Revolution in Parametric Form152 : Introduction to Conic Sections153 : Conic Sections: The Circle154 : Conic Sections: The Ellipse part 1 of 2155 : Conic Sections: The Ellipse part 2 of 2156 : Conic Sections: The Parabola part 1 of 2157 : Conic Sections: The Parabola part 2 of 2158 : Conic Sections: The Hyperbola part 2 of 2159 : Determining What Type of Conic Section from General Form160 : Introduction to Polar Coordinates161 : Animation: Comparing Polar and Rectangular Coordinates162 : Converting Polar Equations to Rectangular Equations163 : Graphing Polar Equations I164 : Graphing Polar Equations II165 : Animation: Graphing Polar Equations166 : Graphing Conic Sections Using Polar Equations - Part 1167 : Graphing Conic Sections Using Polar Equations - Part 2168 : Graphing Conic Sections Using Polar Equations - Part 3169 : Area Using Polar Coordinates - Part 1170 : Area Using Polar Coordinates - Part 2171 : Area Using Polar Coordinates - Part 3172 : Area Bounded by Two Polar Curves - Part 1173 : Area Bounded by Two Polar Curves - Part 2174 : The Slope of Tangent Lines to Polar Curves175 : Horizontal and Vertical Tangent Lines to Polar Curves176 : Arc Length of a Polar Curve177 : Surface Area of the Revolution of a Polar Curve178 : Introduction to Vectors179 : Vector Operations180 : The Unit Vector181 : Vectors: Applications182 : Determining the Angle Between Two Vectors183 : Proving the Formula for the Angle Between Two Vectors184 : Vector Projection185 : Proving the Vector Projection Formula186 : Vector Applications: Force and Work187 : Plotting Points in 3D188 : The Equation of a Sphere189 : Vectors in Space190 : Parallel Vectors191 : Vector Cross Products192 : An Application of Cross Products: Torque193 : The Triple Scalar Product194 : Parametric Equations of a Line in 3D195 : Determining the Equation of a Plane196 : Graphing a Plane on the XYZ Coordinate System197 : Determining the Angle Between Two Planes198 : Determining the Distance Between a Plane and a Point199 : Determining the Distance Between a Line and a Point200 : Cylindrical Surfaces201 : Introduction to Quadric Surfaces202 : Quadric Surface: The Ellipsoid203 : Quadric Surface: The Hyperboloid of One Sheet204 : Quadric Surface: The Hyperboloid of Two Sheets205 : Quadric Surface: The Elliptical Cone206 : Quadric Surface: The Elliptical Paraboloid207 : Quadric Surface: The Hyperbolic Paraboloid208 : Surfaces of Revolution209 : Introduction to Cylindrical Coordinates210 : Converting Between Cylindrical and Rectangular Equations211 : Introduction to Spherical Coordinates212 : Converting Between Spherical and Rectangular Equations213 : Introduction to Vector Valued Functions214 : The Domain of a Vector Valued Function215 : Determining a Vector Valued Function from a Rectangular Equation216 : Determine a Vector Valued Function from the Intersection of Two Surfaces217 : Limits of Vector Valued Functions218 : The Derivative of a Vector Valued Function219 : Determining Where a Space Curve is Smooth from a Vector Valued Function220 : Integrating Vector Valued Functions221 : Properties of the Derivatives of Vector Valued Functions222 : The Derivative of the Cross Product of Two Vector Valued Functions223 : Determining Velocity, Speed, and Acceleration Using a Vector Valued Function224 : Determining the Unit Tangent Vector225 : Determining the Unit Normal Vector226 : Proving the Unit Normal Vector Formula227 : Determining a Tangent Line to a Curve Defined by a Vector Valued Function228 : Determining the Tangential and Normal Components of Acceleration229 : Determining Arc Length of a Curve Defined by a Vector Valued Function230 : Determining Curvature of a Curve Defined by a Vector Valued Function231 : Determining the Binormal Vector232 : Introduction to Functions of Two Variables233 : Level Curves of Functions of Two Variables234 : Limits of Functions of Two Variables235 : First Order Partial Derivatives236 : Second Order Partial Derivatives237 : Differentials of Functions of Two Variables238 : Applications of Differentials of Functions of Several Variables239 : The Chain Rule for Functions of Two Variable with One Independent Variable240 : The Chain Rule for Functions of Two Variable with Two Independent Variables241 : Implicit Differentiation of Functions of One Variable Using Partial Derivatives242 : Partial Implicit Differentiation243 : Directional Derivatives244 : The Gradient245 : Determining a Unit Normal Vector to a Surface246 : Verifying the Equation of a Tangent Plane to a Surface247 : Determining the Equation of a Tangent Plane248 : Determining the Relative Extrema of a Function of Two Variables249 : Absolute Extrema of Functions of Two Variables250 : Applications of Extrema of Functions of Two Variables I251 : Applications of Extrema of Functions of Two Variables II252 : Applications of Extrema of Functions of Two Variables III253 : Lagrange Multipliers - Part 1254 : Lagrange Multipliers - Part 2255 : Integrating Functions of Two Variables256 : Introduction to Double Integrals and Volume257 : Evaluating Double Integrals258 : Double Integrals and Volume over a General Region - Part 1259 : Double Integrals and Volume over a General Region - Part 2260 : Average Value of a Function of Two Variables261 : Fubinis Theorem262 : Setting up a Double Integral Using Both Orders of Integration263 : Double Integrals: Changing the Order of Integration264 : Double Integrals: Changing the Order of Integration - Example 1265 : Double Integrals: Changing the Order of Integration - Example 2266 : Introduction to Double Integrals in Polar Coordinates267 : Double Integrals in Polar Coordinates - Example 1268 : Double Integrals in Polar Coordinates - Example 2269 : Area Using Double Integrals in Polar Coordinates - Example 1270 : Area Using Double Integrals in Polar Coordinates - Example 2271 : Introduction to Triple Integrals272 : Evaluating Triple Integrals - Example273 : Triple Integrals and Volume - Part 1274 : Triple Integrals and Volume - Part 2275 : Triple Integrals and Volume - Part 3276 : Application of Triple Integrals: Mass277 : Changing the Order of Triple Integrals278 : Triple Integrals Using Cylindrical Coordinates279 : Triple Integral and Volume Using Cylindrical Coordinates280 : Rewrite Triple Integrals Using Cylindrical Coordinates281 : Introduction to Triple Integrals Using Spherical Coordinates282 : Triple Integrals and Volume using Spherical Coordinates283 : Double Integral: Change of Variables Using the Jacobian284 : Example of a Change of Variables for a Double Integral: Jacobian285 : Triple Integrals: Change of Three Variables Using the Jacobian286 : Introduction to Vector Fields287 : The Divergence of a Vector Field288 : The Curl of a Vector Field289 : Conservative Vector Fields290 : Defining a Smooth Parameterization of a Path291 : Line Integrals in R^2292 : Line Integrals in R^3293 : Line Integral of Vector Fields294 : Line Integrals in Differential Form295 : Determining the Potential Function of a Conservative Vector Field296 : The Fundamental Theorem of Line Integrals - Part 1297 : The Fundamental Theorem of Line Integrals - Part 2298 : Fundamental Theorem of Line Integrals - Closed Path299 : Greens Theorem - Part 1300 : Greens Theorem - Part 2301 : Determining Area using Line Integrals302 : Flux Form of Greens Theorem303 : Parameterized Surfaces304 : Area of a Parameterized Surface305 : Surface Integrals with Explicit Surface Part 1306 : Surface Integrals with Explicit Surface Part 2307 : Surface Integrals with Parameterized Surface - Part 1308 : Surface Integrals with Parameterized Surface - Part 2309 : Surface Integral of a Vector Field - Part 1310 : Surface Integral of a Vector Field - Part 2311 : Stokes Theorem - Part 1312 : Stokes Theorem - Part 2313 : The Divergence Theorem - Part 1314 : The Divergence Theorem - Part 2

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Courses Index
1 : Algebra I Review - High School   (Salman Khan / Khan Academy)
2 : Geometry   (Multiple Instructors / Brightstorm)
4 : Geometry – Worked Examples   (Salman Khan / Khan Academy)
5 : Fundamentals of Geometry   (James Sousa / MathIsPower4U)
6 : Algebra II   (Multiple Instructors / Brightstorm)
7 : Algebra II – 10th grade   (Derek Owens / Derek Owens)
8 : Algebra I - Martin Gay Textbook   (Julie Harland / MathGal)
9 : Algebra II - 2008 Prentice Hall Algebra 2 Textbook   (Brad Robb / WowMath)
10 : Algebra II – Worked Examples   (Salman Khan / Khan Academy)
11 : Algebra II - Worked Problems   (Brad Robb / WowMath)
12 : Pre-Calculus   (Multiple Instructors / Brightstorm)