Thanx! Determine the definite integral I = 3x3 + x - 1 / x2(x2 + 1) dx. The corr

Question

Thanx!

Determine the definite integral I = 3x3 + x - 1 / x2(x2 + 1) dx. The correct answer is ln root3 + 1 / root3 + 1 - pi / 12 ln 2 root3 + 1 / root3 + 1 + pi / 12 ln 2root3 + 1 / root3 - 1 + pi / 12 ln root3 - 1 / root3 -1 - pi / 12 None of the above. Evaluate the following definite integral I = 1 / x2 + 2x dx. The correct answer is 1 / 2 ln 3 3 ln 2 / 3 1 / 2 ln 3 / 2 1 / 2 ln 4 / 3 None of the above. Evaluate the improper integral I = e-pi / infinity / x2 dx. The correct answer is - 1 / pie 1 / pi 1 / pi (1 - 1 / e) -1 / pi (1 / e + 1) None of the above. Determine the following indefinite integral I = int root9 - x2 / x2 dx. The correct answer is -root9 - x2 / x2 + root9 - x2 / x + arcsin x2 / 9 + c -arcsin x / 3 + x2 + c -root9 - x2 / x2 - arcsin x / 3 + c -root9 - x2 / x - arcsin x / 3 + c None of the above. Determine the indefinite integral: I = int 2 / 1 + cos theta dtheta. The correct answer is -2 cot theta + 2cosectheta + c 2 cot theta

Explanation / Answer

11. Int ( 4 x^3 + 2x / (x^2 (x^2 + 1)) - (x^3 + x + 1)/ ( (x^2 (x^2 + 1)) }

=INT ( d (x^2 (x^2 + 1)) - x (x^2 + 1)/ (x^2 (x^2 + 1)) - 1/ (x^2 (x^2 + 1)) )

=INT (d (x^2 (x^2 + 1)) - 1/x - 1/x^2 + 1/(x^2 + 1))

= (x^2 (x^2 + 1)) - ln x + 1/x + tan (inverse) x

take the limits and your answer will be

option (3).

12. answer is of form 0.5 * ln((z-1)/(z+1)) from 3 to 2

answer is option 3

13. answer is of form (e^ -(pi * z ) )/pi where z is from 0 to 1/pi

the answer is (1 - 1/e )/ pi --> option 3

14. Let x = 3 sin theta. Eventually you will get, after integration tan(theta) - theta

after putting limits, you will get option 4

15. Multiply num and deno with 1 - cos (theta)

ultimately you will get INT ( cosec ^2(theta) - cosec(theta) cot(theta))

integrating you get answer option 1

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