Question

Evaluate the integral.

Answer 1

8/ln(9)

Explanation:

Let u=cos(x). Then du=-sin(x) dx.

If x=0, then u=cos(0)=1.

If x=pi/2, then ucos(pi/2)=0.

The intgral is rewriten as

Integrate((9^u (-du) , from u=1 to u=0)

-9^u/ln(9) |u=1..0)

Upperlimit goes in first no matter if it is tinier in value:

(-9^0/ln(9)--9^1/ln(9))

-1/ln(9)+9/ln(9)

8/ln(9)