SOLUTION: Please help me solve this equation. Evaluate the following definite integral: {{{ int( 2(cos y+1/y), dy, 1, pi ) }}}

SOLUTION: Please help me solve this equation. Evaluate the following definite integral: {{{ int( 2(cos y+1/y), dy, 1, pi ) }}}

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Question 344493: Please help me solve this equation. Evaluate the following definite integral:
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Using some basic properties of integrals we can factor out the 2:

and separate it into two:

Now we have two fairly simple integrals. Since cos(y)dy integrates to sin(y) and (1/y)dy integrates to ln(y) we should get:

Since and ln(1) = 0:

Simplifying:

If you need a decimal answer, then make sure your calculator is set to radian mode when you find sin(1).

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