Khan Academy
Khan Academy: Calculus: Example of Closed Line Integral of Conservative Field
Video lesson solving a closed line integral by first showing that the vector field is conservative and then knowing based on the information in the previous video that the closed line integral is equal to zero. [11:02]
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Khan Academy: Calculus: Green's Theorem Proof (Part 2)
Video finishing the derivation of Green's theorem by showing that the closed line integral in a vector field with vectors only in the y-direction is equal to the double integral over the region contained within the closed curve of the...
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Khan Academy: Calculus: Example of Calculating a Surface Integral Part 2
Part 2 of a 3-part video series showing how to calculate the surface integral of a torus. Video continues to find the surface area of the torus by calculating a cross product. [10:29]
Khan Academy
Khan Academy: Calculus: Line Integral Example 2 (Part 2)
Video lesson continuing the problem from the previous video on finding the surface area along a closed curve using line integrals. Two line integrals are set up and solved and added to the area found previously. [9:58]
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Khan Academy: Calculus: Conceptual Clarification for 2 D Divergence Theorem
Video revisits the 2-D divergence theorem to involve mass density and velocity and find the mass exiting the closed curve. [9:28]
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Khan Academy: Calculus: Calculus: Derivatives 1
Video introducing a derivative as the slope of a tangent line by reviewing the concept of the slope of a line and using that to find the slope of a secant line. Includes link to additional practice problems. [9:25]
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Khan Academy: Brain Teasers: Blue Forehead Room
Video explains the following brain teaser: One-hundred perfect logicians are blindfolded and each has their forehead painted blue. They all enter a room with the lights off, sit in a circle, and the lights are turned on. Each logician...
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Khan Academy: Calculus: Example of Calculating a Surface Integral Part 3
This is part 3 of a 3-part video series showing how to calculate the surface integral of a torus.
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Khan Academy: Calculus: Calculus Bc 2008 #2B & C
Video lesson solving the second part and the third part of a free response problem from the 2008 AP Calculus BC exam about people waiting in line to purchase tickets. Solution requires finding a trapezoidal sum and critical points. [10:42]
Khan Academy
Khan Academy: Calculus: Ap Calculus Bc Exams: 2008 #1D
Video lesson solving the fourth part of a free response problem from the 2008 AP Calculus BC exam about finding the area between two curves. Solution involves finding the volume of a solid whose cross-sections are rectangles using...
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Khan Academy: Calculus: Proof: D/dx (E^x) = E^x
Video lesson proving the derivative of the e^x by using the derivative of the natural logarithm of x function. Includes link to additional practice at the top of the video. [4:40]
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Khan Academy: Calculus: Green's Theorem Example 2
Video lesson solving the line integral of a region formed by the unit circle by using Green's theorem. Accounts for region being formed by moving in a clockwise direction instead of the counterclockwise direction. [7:07]
Khan Academy
Khan Academy: Calculus: Integrals: Trig Substitution 3 (Long Problem)
Video lesson solving an indefinite integral by substituting trigonometric identities. Part of the solution involves completing the square. [17:52]
Khan Academy
Khan Academy: Calculus: Line Integrals and Vector Fields
Video that first reviews the concept of work, then gives a vector field and sets up a line integral to find the work done on a particle moving along a path using a dot product. [16:46]
Khan Academy
Khan Academy: Calculus: Double Integrals 2
Video lesson showing how to compute the double integral to find the volume under a specific surface defined as a function of x and y. Includes a visual representation. [9:50]
Khan Academy
Khan Academy: Calculus: Double Integrals 4
Video lesson showing an alternate way to understand double integrals by integrating with respect to A instead of x and y in order to find the volume under a surface. [9:24]
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Khan Academy: Calculus: Surface Integral Ex1 Pt2: Calculate Surface Differential
Part 2 of a 3-part video series showing how to calculate the surface integral of the unit sphere.. Video calculates the cross product of the two vectors and its magnitude. [12:50]
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Khan Academy: Trigonometry: Iit Jee Trigonometric Maximum
Video demonstrates finding the maximum of a trigonometric expression that is simplified by using trigonometric identities. [9:54]
Khan Academy
Khan Academy: Calculus: 2011 Calculus Ab Free Response #6C
Video shows how to find the integral of a piecewise function and use it to determine the average value of the function over a given interval. [7:29]
Khan Academy
Khan Academy: Calculus: Ap Calculus Bc Exams: 2008 #1A
Video lesson demonstrating the solution to the first part of a free response problem from the 2008 AP Calculus BC exam about finding the area between two curves. [8:54]
Khan Academy
Khan Academy: Calculus: Constructing a Unit Normal Vector to a Surface
Video showing how to construct the unit normal vector to a surface for any point on a curve by first showing how to find any normal vector and from there finding the unit normal vector. Includes an explanation of how to find the...
Khan Academy
Khan Academy: Calculus: Line Integral Example 1
Video lesson showing how to visualize, set up, and solve a line integral. Integral is solved using u-substitution. [13:02]
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Khan Academy: Calculus: Surface Integral Ex1 Pt3: The Home Stretch
Part 3 of a 3-part video series showing how to calculate the surface integral of the unit sphere. Video calculates the double integral of the magnitude of the cross product found in the previous part. Trigonometric identities and...
Khan Academy
Khan Academy: Calculus: 2011 Calculus Bc Free Response #1D
Video shows how to derive the arc length formula and how to use it to determine the total distance a particle traveled during a given time interval. [8:34]