Calculadora de integrales definidas e impropias
Calcular integrales definidas e impropias paso a paso
La calculadora intentará evaluar la integral definida (es decir, con límites de integración), incluyendo las impropias, mostrando los pasos.
Solution
Your input: calculate $$$\int_{0}^{\pi}\left( b d m o \sin{\left(x \right)} \cos{\left(x \right)} \right)dx$$$
First, calculate the corresponding indefinite integral: $$$\int{b d m o \sin{\left(x \right)} \cos{\left(x \right)} d x}=\frac{b d m o \sin^{2}{\left(x \right)}}{2}$$$ (for steps, see indefinite integral calculator)
According to the Fundamental Theorem of Calculus, $$$\int_a^b F(x) dx=f(b)-f(a)$$$, so just evaluate the integral at the endpoints, and that's the answer.
$$$\left(\frac{b d m o \sin^{2}{\left(x \right)}}{2}\right)|_{\left(x=\pi\right)}=0$$$
$$$\left(\frac{b d m o \sin^{2}{\left(x \right)}}{2}\right)|_{\left(x=0\right)}=0$$$
$$$\int_{0}^{\pi}\left( b d m o \sin{\left(x \right)} \cos{\left(x \right)} \right)dx=\left(\frac{b d m o \sin^{2}{\left(x \right)}}{2}\right)|_{\left(x=\pi\right)}-\left(\frac{b d m o \sin^{2}{\left(x \right)}}{2}\right)|_{\left(x=0\right)}=0$$$
Answer: $$$\int_{0}^{\pi}\left( b d m o \sin{\left(x \right)} \cos{\left(x \right)} \right)dx=0$$$