Calculus 1 Hour Exam 3 - Math 220 Fall, 2011

1.	Suppose that f is an odd function which is integrable on the interval [-5,5]. If 2 3 ∫ f(x) dx = 4 and ∫ f(x) dx = 10, then evaluate the following quantities. 0 2 5 3 2 2 a. ∫ f(x) dx + ∫ f(x) dx b. ∫ f(x) dx c. ∫ | f(x) | dx 0 5 -2 -2 Answers: a. 14 b. 0 c. 8
2.	18 1 Evaluate the definite integrals. a. ∫ (1/2x) dx b. ∫ 8 / (1 + x^2) dx 2 0 Answers: a. ln 3 b. 2π
3.	Evaluate the indefinite integrals. a. ∫ (12x / (1 + 3x^2) dx b. ∫ tan x sec^5 x dx Answers: a. 2 ln(1 + 3x^2) + C b. (1/5) sec^5 x + C
4.	Evaluate the indefinite integral ∫ 2x^5 (x^2 + 1)^35 dx Answer: (1/38) (x^2 + 1)^38 – (2/27) (x^2 + 1)^37 + (1/36) (x^2 + 1)^36 + C
5.	Let R be the finite region bounded by the graph of f(x) = 5x - x^2 and the x-axis on the interval [0,5]. Set up, but do not evaluate, definite integrals which represent the given quantities. Use proper notation. a. The average value of f on the interval [0,5] b. The area of R c. The volume of the solid obtained by revolving R around the horizontal line y=-10. d. The volume of the solid obtained by revolving R around the vertical line x=8. 5 5 Answers: a. (1/5) ∫ (5x – x^2) dx b. ∫ (5x – x^2) dx 0 0 5 5 c. ∫ π ( 5x – x^2 + 10 ) ^2 – π (10)^2 ) dx d. ∫ 2π (8 – x) (5x – x^2) dx 0 0 Click here to continue with this exam.

Return to "Hints and Answers to Exams"

Return to Table of Course Notes