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 get:$$\int _ { 0 } ^ { 1 } 9 x \sin \pi x d x = \left [ -9x \frac { \cos \pi x } { \pi } \right ] _ { 0 } ^ { 1 } + \int _ { 0 } ^ { 1 } \frac { 9 } { \pi } \cos \pi x d x$$$$= -9 \frac { \cos \pi } { \pi } + \frac { 9 } { \pi } \left [ \frac { \sin \pi x } { \pi } \right ] _ { 0 } ^ { 1 }$$$$= -9 \frac { ( -1 ) } { \pi } + \frac { 9 } { \pi } \left [ \frac { 0 } { \pi } - \frac { 0 } { \pi } \right ]$$$$= \frac { 9 } { \pi }$$$$= 2.8665$$

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

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