Question

sinx². cosx integrat this question​

Answer 1

AnswEr :

We have to integrate sin²x cos x with respect to x

Now,

$\displaystyle \: \sf \: l = \int \: ({sin}^{2} x.cos \: x)dx$

Let u = sin x

Differentiating both sides,

$\longrightarrow \sf \: du = cos \: x.dx \\ \\ \longrightarrow \: \boxed{ \sf \: dx = \frac{du}{cos \: x} }$

Thus,

$\dashrightarrow \displaystyle \: \sf \:l = \int {u}^{2} \cancel{cos \: x}. \dfrac{du}{ \cancel{cos \: x}} \\ \\ \dashrightarrow \: \sf \: l = \dfrac{ 1}{3} {u}^{3} + c \\ \\ \dashrightarrow \: \boxed{ \boxed{ \sf \: l = \dfrac{1}{3} {sin}^{3} x + c}}$