Evaluate the integral.
-$\int _ { 0 } ^ { \pi / 2 } x \cos x d x$
A) 1
B) $\frac { \pi } { 2 }$ - 1
C) 0
D) π/2

Question

Evaluate the integral. 
-$\int _ { 0 } ^ { \pi / 2 } x \cos x d x$
A) 1
B) $\frac { \pi } { 2 }$ - 1
C) 0
D) π/2

Quizplus · Accepted Answer

This integral can be solved using integration by parts, where $u = x$ and $dv = \cos(x)dx$. The formula for integration by parts is $\int u dv = uv - \int v du$. Applying this, we get $x \sin(x) |_{0}^{\pi/2} - \int_{0}^{\pi/2} \sin(x) dx$, which simplifies to $(\pi/2) - 1$.

Evaluate the Integral ∫0π/2xcos⁡xdx\int _ { 0 } ^ { \pi / 2 } x \cos x d x∫0π/2​xcosxdx

Evaluate the Integral $\int _ { 0 } ^ { \pi / 2 } x \cos x d x$