5. (4pts each)Evaluate the following integrals. s sins (1) cos (1) dx a. dx b. sz...
integration by parts 8. Evaluate the following integrals S cos cos(*)sinº (x)dx b zsin (x)dx
Evaluate the integral 5*7* (sins 2x)(cos 2x) dx by substitution method.
4. Evaluate the definite integrals: A) |_ In xdx 1 xV1+ ln² x I dx cos x sin x a f / Inx di -d
1 (a) Evaluate the integral sz? dx. (32-7) 5 2 7 (b)if s f(x)dx = 3 and 5 f(x)dt = 4, find S f(x)dr. 5
1. Evaluate the integral S77® (sins 2x)(cos 2x) dx by substitutior method.
1. Evaluate each of the following indefinite integrals. 6 Idx b. S [2 cost – 5 sin t]dt x*- x -dx c. d. I cotx sec?x dx
2. Evaluate the following integrals. (a) [5 marks] | el cos 4xdx -1 x (b) [5 marks] / cosdx -x³+3x²-x- dr. 1dx (c) [10 marks] (п -3)(12+2) 4 (d) [5 marks]/ dx V4-5x-2x2 dx cosh x-sinh x (e) [5 marks]] (Give the final answer in terms of e.)
Problem 2. Evaluate each of the following integrals. a) In(4x) dx 1 4x+1 dx ex b) Jo c) S (5x-2)e 6x dx
Evaluate the following integrals. Integral x*ln(x^2+3x+2)dx 2. (8 points) Evaluate the following integrals. Answers without supporting work will re- ceive no credit. (a) (5 points) | < ln(x2 + 3x + 2) dx
11. (4pts) Use the LIMIT DEFINITION of the integral to evaluate the following integrals. No Credit will be awarded for solutions obtained by using the Fundamental Theorem of Calculus. [ (2-x²)dx