Evaluate.

Question

int_(pi)^(pi) (sin(x))^(3) (cos(x))^(3) dx

Answer 1

int_(pi)^(pi) (sin(x))^(3) (cos(x))^(3) dx
Omitting the π², we have
∫sin³(x)cos³(x)dx
=∫sin³(x)(1-sin²(x))cos(x)dx
=∫sin³(x)(1-sin²(x))dsin(x)
=sin^4(x)/4-sin^6(x)

Answer 2

no the answer is not that

Answer 3

it should be zero because its pi-pi

Answer 4

I have evaluated the indefinite integral.
If the limits are indeed π to π, yes, the answer is zero.

You have posted π^π, which I am not sure what it means, that is why I have indicated: "ignoring π^π".

It appeared to me that it is a constant equal to π², which doesn't make any sense.

Sorry that I have omitted the important term " +C " which indicates that it is an indefinite integral.

Answer 5

its okay, thank you for all your help i really appreciated it!