Math. 69.104A

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1. Evaluate the derivative of the integral of the function f(x) = x sin (Pi*x) between the variable limits, x = t, and x = 2t. What is the value of this derivative when t=1/2?

1

-1/2

1/2

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2. Find the area under the curve whose equation is given by f(x) = |x^2 - 1| between x = -1 and x = 1 (Note: This is the "absolute value of the function x squared minus one")

4/3

0

2/3

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3. Find the area under the curve whose equation is given by f(x) = |x^2 - 1| between x = -1 and x = 2 (Note: This is the "absolute value of the function x squared minus one

3

4/3

8/3

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4. What is the indefinite integral of the function f(t) = (t^2) sin(t^3) whose value at t = 0 is equal to 0 ?

(1 - cos(t^3)) / 3

-cos(t^3) + constant

-cos(t^3) + 1

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