Name: College ID: Thomas Edison State College Calculus II (MAT-232) Section no.: Semester and year: Written Assignment 2 Answer all assigned exercises, and show all work. Each exercise is worth 4 points. Section 6.2 4. Evaluate the integral. x ln x dx 6. Evaluate the integral. ln x dx x 18. Evaluate the integral. 2 x sin x dx 22. Evaluate the integral. 1 2 3x xe 0 WA 2, p. 1 dx 24. Evaluate the integral. 2 x ln x dx 1 46. Evaluate the integral using integration by parts and substitution. 2 x ln(4 +x ) dx Section 6.3 8. Evaluate the integral. sin 4 ( x - 3) dx 10. Evaluate the integral. cot x csc 4 x dx 18. Evaluate the integral. (cos 2 x +sin 2 x) dx 28. Evaluate the integral. x 3 x 2 - 1 dx 30. Evaluate the integral. x x2 - 4 dx Section 6.4 2. Find the partial fractions decomposition and an antiderivative. 5x - 2 x2 - 4 12. Find the partial fractions decomposition and an antiderivative. 1 x +4 x 3 16. Find the partial fractions decomposition and an antiderivative. 2x x - 6 x +9 2 22. Evaluate the integral. x 2 +1 x 2 - 5 x - 6 dx 24. Evaluate the integral. x 1 dx -1 3 WA 2, p. 3 Section 6.6 8. Determine whether the integral converges or diverges. Find the value of the integral if it converges. 1 (a) - 0 x 2e3 x dx (b) - xe - 4 x dx 10. Determine whether the integral converges or diverges. Find the value of the integral if it converges. (a) 0 cos x dx (b) 0 cos xe - sin x dx 16. Determine whether the integral converges or diverges. Find the value of the integral if it converges. 2 0 (a) x dx 2 x -1 Section 3.2 2. Find the indicated limit. lim x 2 x2 - 4 x 2 - 3 x +2 12. Find the indicated limit. tan x - x 0 x3 lim x (b) 0 1 dx ( x - 2) 2 14. Find the indicated limit. lim t 1 ln t t-1 22. Find the indicated limit. lim x ln x x 30. Find the indicated limit. lim x 0+ x ln x 38. Find the indicated limit. lim (cos x)1/ x x 0+ WA 2, p. 5