What is the integral using the substitution u=sin(2x)?

find π40sin4(2x)cos(2x)dx using the substitution u=sin(2x)

1 Answer
May 29, 2018

I=110

Explanation:

We want to integrate

I=π40sin4(2x)cos(2x)dx

Make a substitution u=sin(2x)du=2cos(2x)dx
New limits x=0u=0 and x=π4u=1

I=1210u4du=[110u5]10=110