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Contents

Review of Calculus BC II

Review Test

Table of Contents

Further Reading

Compute e sin(x)cos(x)dx .

Find tan(x)dx .

Compute 1/()dx .

Compute 2sin(x)cos(x)dx .

Find

dx    

Compute x 2 e x3+7 dx .

In order to integrate a function that is a product of an easily integrable function with an easily differentiable one, it is often useful to employ

The method of integration that is closely related to the chain rule for differentiation is the

Compute 5xe x dx .

Compute (log(x))2/xdx .

Find - 4dx

Compute 3 - | x + 1| dx .

Determine the value of Π/x 2 dx .

Find 2 dx .

Compute the area between the graphs of the functions f (x) = x 2 - 4x + 3 and g(x) = - x 2 + 4x - 3 .

Find the area between the graphs of x 2 - 3 and 2x - 3 .

Find the volume of the solid given by revolving the region below the graph of 6 - 3x from 0 to 2 about the y -axis.

Compute the volume of the solid given by revolving the region below the graph of x 2 - 4x + 5 from x = 0 to 2 about the y -axis.

Compute the volume of the solid given by revolving the region below the graph of sin(x) from 0 to Π about the y -axis.

Compute the volume of the solid given by revolving the region below the graph of sin(x) from 0 to Π about the x -axis.

Determine the volume of the solid given by revolving the region below the graph of e 2x from x = 1 to 2 about the x -axis.

Compute the volume of the solid given by revolving the region below the graph of f (x) = 2 from x = - 2 to 1 about the x -axis.

Find sin(x)e x dx .

Compute x 4log(x)dx .

Find the value of cos2(x)(1 + tan2 x)dx .

Determine the radius of convergence of 5(- 1)n x n .

What is the radius of convergence of (x - 1)n/n! ?

Find the integral of (- 1)n-1 x n/n (on its radius of convergence).

What is the value of 6(1/3)n ?

Compute

dx    

Compute

dx    

Find

dx    

Compute

dx    

Compute 1/(x - 1)2 .

Find x/(x - 1)2 dx .

It is possible for a series with positive terms to converge but not

Determine the value of 1/(n log(n)) .

Find 1/(x(log(x))2)dx .

For which values of k does the series 4/(n + 1)k converge?

The Taylor series of a function is a kind of

Find the length of the parametric curve (3 + 2 sin(t), -1 + 2 cos(t)) from t = 0 to Π .

How many petals are on the "flower" formed by the polar curve r(θ) = sin(4θ) ?

What is the velocity vector to the parametric curve (e t + cos(t), 3t + 2) at time t = 2Π ?

Find the acceleration vector for the parametric curve (sin(t)cos(t), log(t)) at time t .

Find the speed of the particle whose motion in the plane is given by (log(27x 2), 3x) .

Determine the area below the polar curve r(θ) = 3θ 2 + 2 from θ = 0 to 1 .

Compute the area below the graph of the polar curve r(θ) = e θ from θ = 2 to t .

Find the area between the parametric curves (t, t 2 - 1) and (t, - t 2 + 1) .

The set of points on a unit circle could not be

To derive the formula for the length of the parametric curve, one may

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