Khan Academy
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...
Khan Academy
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]
Khan Academy
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]
Khan Academy
Khan Academy: Calculus: Vector Valued Function Derivative Example
Video lesson solving for the derivatives for a two specific vector-valued functions that describe the same path but have different velocities. [12:45]
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Khan Academy: Calculus: Triple Integrals 1
Video lesson introducing triple integrals by finding the volume of a rectangular prism. [10:38]
Khan Academy
Khan Academy: Calculus: Triple Integrals 2
Video explaining how to use triple integrals to find the mass of a rectangular prism with variable density. [7:26]
Khan Academy
Khan Academy: Calculus: Error or Remainder of a Taylor Polynomial Approximation
Video first reviews the formula for a Taylor series expansion and then defines the error function to be the difference between the polynomial approximation and the actual function. Properties of the derivatives of the error function are...
Khan Academy
Khan Academy: Calculus: Surface Integral Ex3 Pt3: Top Surface
Part 3 of a 4-part video series solving for the surface integral of a surface made of three separate parts. The third video parametrizes the third surface, finds the magnitude of the cross product and begins to evaluate the double...
Khan Academy
Khan Academy: Brain Teasers: Light Bulb Switching Brain Teaser
Video explains how to solve the following brain teaser: One hundred light bulbs are arranged in a row. Each light bulb can be either on or off. On the first pass of the row, each bulb is switched on. On the second pass, every other bulb...
Khan Academy
Khan Academy: Brain Teasers: 3 D Path Counting Brain Teaser
Video explains how to solve the following brain teaser: Starting in the upper left rear block of a 3x3 cube, how many different ways are there to get to the bottom right front block of the cube, with movement restricted to moving to the...
Khan Academy
Khan Academy: Calculus: 2011 Calculus Bc Free Response #1A
Video shows how to find the velocity and acceleration vectors of a particle at a given time by using the derivatives of the parametric equations representing the particle. Also shows how to find the magnitude of the velocity vector in...