Question

Calcule as integrais por substituição de variável

Answer 1

Bom dia Lucas!


Solução!


$\displaystyle \int \sqrt{senx}.cosxdx\\\\\\ u=senx~~~~du=cosxdx\\\\\\\\ \displaystyle \int \sqrt{u}\\\\\\\\\ Fazendo!\\\\\\\ \sqrt{u}=(u)^{ \frac{1}{2}}= \frac{(u)^{ \frac{1}{2}+1 } }{ \frac{1}{2} +1}=\frac{(u)^{ \frac{3}{2} } }{ \frac{3}{2} }= \frac{2}{3} \sqrt{(u)^{3} }\\\\\\\\\ \frac{2}{3} \sqrt{(u)^{3} }+c\\\\\\\\\ \frac{2}{3} \sqrt{(senx)^{3} }+c\\\\\\\\\ \boxed{Resposta:\displaystyle \int \sqrt{senx}.cosxdx= \frac{2}{3} \sqrt{(senx)^{3} }+c}$


Boa tarde!
Bons estudos!

Answer 2

∫$\sqrt{senx}.cosxdx$

u = senx
du = cosxdx

∫√u . du

∫$u^{ \frac{1}{2} } du$

$\frac{ u^{ \frac{3}{2} } }{ \frac{3}{2} }$

$\frac{2}{3}. u^{ \frac{3}{2} }$

$\frac{2}{3}. (senx)^{ \frac{3}{2} }+c$