6 Questions in Exam 1 - Calculus II | MATH 121, Exams of Calculus

Download 6 Questions in Exam 1 - Calculus II | MATH 121 and more Exams Calculus in PDF only on Docsity! Calculus II – Math 121 Spring 2005 Test #1 Name: (print neatly) Instructor: (sign) This exam is CLOSED NOTES and CLOSED BOOK. There are NO CALCULATORS allowed. To get full credit you must show all work neatly in the space provided on the test paper. 1. [10 pts each] Compute the following integrals: a. ∫ 5x2 − 3 +√x + 1 2 √ x dx b. ∫ x2 sin(3− x3) dx c. ∫ sin(t)(cos2(t) + 1) dt 1 of 6 d. ∫ 2 0 √ x− √ 2 dx e. ∫ 2 1 t− t−1 t4 dt f. ∫ sec2(θ + π) dθ 2 of 6 5. [8 pts] Suppose f(x) is a continuous function defined on [1, 3] with −1 < f(x) < 2. a. Show that it must be true that ∫ 2 1 3 + f(x) + 2[f(x)]2 dx < 30. b. Give an example of to show that it may be true that ∫ 2 1 3 + f(x) + 2[f(x)]2 dx > 10. 5 of 6 6. [8 pts] The function f(x) is pictured below. Let A(x) = ∫ x 0 f(t) dt be the accumulation function. 6 - 1 2 3 4 x 1 2 3 y f(x) @ @ @ @ @ a. Circle the letter of the correct graph of A(x) below. A) 6 - 1 2 3 4 x 1 2 3 y A(x) B) 6 - 1 2 3 4 x 1 2 3 y A(x) C) 6 - 1 2 3 4 x 1 2 3 y A(x) ¡ ¡ ¡ ¡ ¡ D) 6 - 1 2 3 4 x 1 2 3 y A(x) ¡ ¡ ¡ ¡ ¡ b. Compute A′(x). 6 of 6