Hello, earthboy!
The first one requires Olympic-level gymnastics.
I hope you're up for it . . .
To the denominator, add and subtract
. .
. .
. .
The integral becomes: .
Let:
Substitute: .
Back-substitute: .
Using the cos(A+B) identity..
Using
gives an incorrect answer for the area between the curve and the x-axis,
since the graph of the function crosses the x-axis twice between and
Hence, the x-axis crossing points are at
and at
Inverting the negative sign for the integral in the middle part, the area is
which gives