Question

Evaluate the integral of (sin³ x + sinxcos²x)dx

Answer 1

We have to find $\int$ (sin³(x) + sin(x)cos²(x)) dx

Let I = $\int$ (sin³(x) + sin(x)cos²(x)) dx

= $\int$ sin(x)(sin²(x) + cos²(x)) dx

= $\int$ sin(x) dx $\because$ sin²(x) + cos²(x) = 1

= - cos(x) + C where C is a constant

hence,

I = - cos(x) + C