Question

Evalaute: ${\int }_{-1}^1\left[x\sin \pi x\right]dx$

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $0$

${\int }_{-1}^1\left[x\sin \pi x\right]dx-1⟶00⟶1f\left(x\right)=\left[xsin\pi x\right]f(-1)=0f\left(0\right)=0f\left(1\right)=0$

The value of $\left[f\right(x\left)\right]$ is $0$ from $-1$ to $1$.

$[\therefore f(x)=(0,1\left)\right]={\int }_{-1}^1\left[x\sin x\right]dx={\int }_{-1}^{1}0dx=0$