Question

Responda a integral $\int\limits^ \pi _0 {cos 2x} \, dx$

Answer 1

Vamos resolver essa integral por substituição, veja:

Façamos a seguinte substituição:

u = 2x;
du = 2 dx

Vejamos:

$\mathsf{\displaystyle\int_{0}^{\pi}~\mathsf{Cos(2x)~dx}}}\\\\\\\\\ \mathsf{\displaystyle\int_{0}^{2\pi}~\dfrac{cos(u)}{2}~du}}\\\\\\\\ \mathsf{\dfrac{1}{2}}~\mathsf{\displaystyle\int_{0}^{2\pi}~cos(u)~du}}}}\\\\\\\\ \mathsf{\dfrac{1}{2}~sin(u)\bigg|_{0}^{2\pi}}}}\\\\\\\\ \mathsf{\dfrac{1}{2}~(sin(2\pi)-sin(0))}}\\\\\\\\ \Large\boxed{\boxed{\boxed{\mathbf{~\therefore~\displaystyle\int_{0}^{\pi}~Cos(2x)~dx}=0.}}}}}}}}}}}}}}}}}}}}}~~\checkmark}}}$

Espero que te ajude. '-'