Quiz 2-sol - Math 116 Name Quiz 2 Evangelos Dimou Section Note Show all your work No calculators allowed 1(5 points Compute the following integrals Z p

Quiz 2-sol - Math 116 Name Quiz 2 Evangelos Dimou Section...

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Math 116 Quiz 2 January 19, 2017 Name: Evangelos Dimou Section: 45/65/85 Note: Show all your work. No calculators allowed. 1. (5 points) Compute the following integrals:(a)Zpcos(3x) sin(3x)dx (b)
2. (5 points) Some values of a functionfand its derivative are given in the tablebelow. Assume thatf0is continuous.x01234f(x)0342-1f0(x)42-1-5-2(a) ComputeZ21tf00(t)dt. SolutionWe integrate by parts:Z21tf00(t)dt=tf(t)21-Z21tf(t)dt= 2f(2)-f(1)-Z21f(t)dt-2-2-(f(2)-f(1)) =-4-(4-3) =-5Z4 (b) Compute3f(x)ef(x)dx. SolutionWe make the substitutionu=f(x). Thendu=f(x)dxand thereforeZ43f(x)ef(x)dx=Zf(4)f(3)eudu=Z-1eudu=eu-12=e-1-e2 2

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