Question

2π
∫ sin³x cos²x dx ,Evaluate it.
0

Answer 1

please see the attachment

Answer 2

Answer:

$\int\limits^{2\pi}_0 {sin^{3}x.cos^{2}x} \, dx = 0$

Step-by-step explanation:

In the given question,

We have been provided the equation to integrate and find the value of,

$\int\limits^{2\pi}_0 {sin^{3}x.cos^{2}x} \, dx$

So, Now let us assume that,

$f(x)=sin^{3}x.cos^{2}x$

So,

The value of,

$f(2\pi - x) =  sin^{3}(2\pi-x).cos^{2}(2\pi-x)$

So, on solving this we get,

$f(2\pi-x)=-sin^{3}x.cos^{2}x=-f(x)$

Therefore,

f(2π - x)= -f(x)

So we can say that the value of the integral will be giving us the value = 0.

Because, the value from 0 to π will be positive and the value from π to 2π will be negative.

Therefore the value of the integral will be 0.

So,

$\int\limits^{2\pi}_0 {sin^{3}x.cos^{2}x} \, dx = 0$