Question

integral from pi to pi sin^4x cos^5x dx how do it evaluate

Answer 1

from -pi to pi?

Answer 2

no both postive

Answer 3

We know the integral from pi to pi is zero. (same limits)
Any integral with lower limit equal to upper limit is zero.

Answer 4

ok so since sin^4x cos^5x dx. this would conculd to be tan^2x?

Answer 5

The indefinite integral can be found by substitution:
u=sin(x)
du = cos(x)dx
and use sin^2(x)+cos^2(x)=1 to convert
sin^4(x)cos^4(x)
=sin^4(x)(1-sin^2(x))^2
=u^4(1-u^2)^2
So
I=integral(u^4(1-u^2)^2du
And you'll soon find that the integral with limits -pi to pi, -pi to 0, 0 to pi all give 0.

Answer 6

To make it more understandable,
\[\int\limits \sin^4(x)\cos^5(x)dx \ = \ \int\limits u^4(1-u^2)^2du\]
with\[u=\sin(x), \ du=\cos(x)dx\]