Question

Question #a2f4c

Answer 1

This list of integrals contains a reduction formula for

`intsin^n(x)dx`

we shall recursively use it.

Explanation:

The reduction formula is:

`intsin^n(x)dx=(sin^(n-1)(x)cos(x))/n+(n-1)/nintsin^(n-2)(x)dx`

Substituting 6 into the formula:

`intsin^6(x)dx=(sin^5(x)cos(x))/6+5/6intsin^4(x)dx`

Substituting 4 into the formula:

`intsin^6(x)dx=(sin^5(x)cos(x))/6+5/6[(sin^3(x)cos(x))/4+3/4intsin^2(x)dx]`

Substituting 2 into the formula:

`intsin^6(x)dx=(sin^5(x)cos(x))/6+5/6[(sin^3(x)cos(x))/4+3/4{(sin(x)cos(x))/2+1/2intdx}]`

We know the last integral:

`intsin^6(x)dx=(sin^5(x)cos(x))/6+5/6[(sin^3(x)cos(x))/4+3/4{(sin(x)cos(x))/2+1/2x}] + C`