Sample Questions, TEST 2:


Dr. Angelo Mingarelli
Department of Mathematics and Statistics
Carleton University
Ottawa, Ontario, Canada, K1S 5B6

Please remember that, due to the presence of older browsers on the Internet, powers will be reproduced by the form "x^2" (which is "x squared"), "x^(sin(x))" (which is "x to the power sin(x)"), etc...

Lastly, there is only one answer per question...

Solutions may be found below, at the end of this page.

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

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

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

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

5. Evaluate the integral of the function f(x) = (x^3) * sin (Pi*x) between the limits, x = 0, and x = 1.
1/Pi - 6/Pi^3
1/Pi + 6/Pi^3
1/2

6. Find the area under the curve whose equation is given by f(x) = (e^3x) * sin (5x) between x = 0 and x = Pi/5
1/34
5*{e^(3*Pi/5) + 1}/34
9*{e^(3*Pi/5) + 1}/34

7. Find the area under the curve whose equation is given by f(x) = sin (3x) * cos (6x) between x = 0 and x = Pi/18
1/108
(9*Sqrt(3) - 12)/108 = 0.0332...
Sqrt(3)/108

8. What is the indefinite integral of the function f(t) = (t^5) ln (2t) whose value at t = 1 is equal to 0 ?
{6(t^6) * ln(2t) - (t^6)}/36
I don't know!
{6(t^6) * ln(2t) - (t^6)}/36 + (1 - 6ln(2)}/36

Solutions are:

END