Evaluate the integral. $\int _ { 0 } ^ { 1 } 9 x \sin \pi x d x$
A) $2.8665$
B) $6.5700$
C) $0.7166$
D) $11.8665$
E) None of these

Question

Quizplus · Accepted Answer

Using integration by parts, we have:$\int _ { 0 } ^ { 1 } 9 x \sin \pi x d x = -9 \left[ x \cos \pi x \right]_0^1 + 9 \int _ { 0 } ^ { 1 } \cos \pi x d x$$\int _ { 0 } ^ { 1 } 9 x \sin \pi x d x = -9 \left[ (1) \cos \pi - (0) \cos 0 \right] + 9 \left[ \frac { 1 } { \pi } \sin \pi x \right]_0^1$$\int _ { 0 } ^ { 1 } 9 x \sin \pi x d x = -9 \left[ -1 \right] + 9 \left[ \frac { 1 } { \pi } (0) - \frac { 1 } { \pi } (0) \right]$$\int _ { 0 } ^ { 1 } 9 x \sin \pi x d x = 9 + 0$$\int _ { 0 } ^ { 1 } 9 x \sin \pi x d x = 9$

Evaluate the Integral ∫019xsin⁡πxdx\int _ { 0 } ^ { 1 } 9 x \sin \pi x d x∫01​9xsinπxdx

Evaluate the Integral $\int _ { 0 } ^ { 1 } 9 x \sin \pi x d x$