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2 Integral questions- Calculus?

+2 votes

Hi there. I was doing my homework and I stumbled upon these two problems that i do not know how to do. If someone could show me how to solve it I would greatly appreciate it. Thank you

Evaluate:
1. ∫ x/(4+x^2) dx

2. ∫ (x^2-x)sinπx dx from 0 to 1 

Thank you

asked Jan 16, 2013 in CALCULUS by skylar Apprentice

2 Answers

+3 votes

1.     ∫ x/(4+x^2) dx

        ∫ x/(x^2+4) dx

       Multiply the above integral with 2/2

       2/2 ∫ x/(x^2+4) dx

      1/2 [ ∫ 2x/(x^2+4) dx]

       Let   f(x)  =  x^2+4

                f`(x) = 2x

            1/2 log(x^2+4)                  ( ∫ f`(x)/f(x) dx = log f(x) )

       ∫ x/(4+x^2) dx = 1/2 log(x^2+4)

answered Jan 16, 2013 by Johncena Apprentice
0 votes

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The solution is -0.129006.

 

answered Jul 4, 2014 by joly Scholar

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