Question

QUAL A INTEGRAL DE S xsen(x)dx??l

Answer 1

Resposta:

Solução:

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \int x \cdot \sin (x) dx \end{array}\right$

Fazendo a integral por partes:

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf u = x \to du = 1 \cdot dx \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf dv = \sin (x) dx \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf v = -\: \cos(x) \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \int u \cdot dv = u \cdot v - \int v \cdot du \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \int x \sin (x) dx = x \cdot (- \cos(x) - \int (- \cos(x) dx \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \int x \sin (x) dx = -\:x \cos(x) +\int \cos(x) dx \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \int x \sin (x) dx = -\:x \cos(x) + \sin(x) +C \end{array}\right$

Explicação passo-a-passo: