Study Guide 3 F_13

# If we use the substitution u x2 11 then which of the

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Unformatted text preview: ndeﬁnite integral: ￿ 3 3x2 ex +2 dx (A) u = 3x2 (B) u = x3 + 2 (C) u = 3 (D) u = x (E) None of these 11. If we use the substitution u = x2 + 11, then which of the following is equivalent to ￿ x(x2 + 11)1/3 dx. (A) (D) ￿ ￿ u 1/3 du (u − 11)1/2 u1/3 du 2 (B) ￿ u 1 /3 du 2 (E) none of these (C) ￿ (u − 11)1/2 u1/3 du 12. Use substitution to ﬁnd the indeﬁnite integral. ￿ 6 dx (6x + 1)2 13. Use substitution to ﬁnd the indeﬁnite integral. ￿ x dx 2 + 4x 2 14. Evaluate the following indeﬁnite integral. ￿ 4e 4 x dx 2 + e 4x (A) e 4x +C 2x + 0.25e4x (B) ln |2 + e4x | + C (D) 1 4x e + 4x + C 2 (E) none of these (C) 4 ln |2 + e4x | − 2 − e4x + C 15. If we use the substitution u = 2x + e−5x , then which of the following is equivalent to ￿ 2 − 5e − 5 x dx. (2x + e−5x )2 (A) ￿ du u (B) ￿ u2 du (C) ￿ du u2 (D) ￿ u du (E) none of these 16. Approximate the area under the graph of f (x) = ex + 1 and above the x-axis from x = −2 to x = 2 with rectangles, using left endpoints, with n = 4. The approximate area is (A) less than 9 (D) between 13 and 15 17. Find arcs. ￿ (B) between 9 and 11 (C) between 11 and 13 (E) more than 15 7 f...
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