Use integration tables to evaluate the integral $\int _ { 0 } ^ { \pi / 2 } 21 x \cos x d x$
A) $21 \pi$
B) $\frac { 21 \pi } { 2 }$
C) $21 \left( \frac { \pi - 1 } { 2 } \right)$
D) $21 ( \pi - 1 )$
E) $21 \left( \frac { \pi } { 2 } - 1 \right)$

Question

Quizplus · Accepted Answer

This integral can be solved using integration by parts, where $u = x$ and $dv = 21\cos(x)dx$. The formula for integration by parts is $\int u dv = uv - \int v du$. After applying this formula and evaluating the definite integral from $0$ to $\pi/2$, the result is $21 \left( \frac { \pi } { 2 } - 1 \right)$.

Use Integration Tables to Evaluate the Integral ∫0π/221xcos⁡xdx\int _ { 0 } ^ { \pi / 2 } 21 x \cos x d x∫0π/2​21xcosxdx

Use Integration Tables to Evaluate the Integral $\int _ { 0 } ^ { \pi / 2 } 21 x \cos x d x$