Question

Calcule a figura abaixo. Por favor

Answer 1

$\large\boxed{\begin{array}{l}\displaystyle\rm\int sen^2(x)\cdot cos^3(x)\,dx=\int sen^2(x)\cdot cos^2(x)\cdot cos(x)\,dx\\\displaystyle\rm\int sen^2(x)\cdot cos^3(x)\,dx=\int sen^2(x)\cdot(1-sen^2(x))\cdot cos(x)\,dx\\\underline{\sf fac_{\!\!\!,}~\!a}\\\rm u=sen(x)\longrightarrow du=cos(x)\,dx\\\displaystyle\rm\int sen^2(x)\cdot cos^3(x)\,dx=\int u^2\cdot(1-u^2)\,du=\int(u^2-u^4)\,du\end{array}}$

$\large\boxed{\begin{array}{l}\displaystyle\rm\int (u^2-u^4)\,du=\dfrac{1}{3}u^3-\dfrac{1}{5}u^5+k\\\displaystyle\rm\int sen^2(x)\cdot cos^3(x)\,dx=\dfrac{sen^3(x)}{3}-\dfrac{sen^5(x)}{5}+k\\\huge\boxed{\boxed{\boxed{\boxed{\rm\dagger\red{\maltese}~\blue{alternativa~E}}}}}\end{array}}$