37. Josin, dr., 2
The given integral is, I = ∫ 0 π 2 sin 3 x d x .
Solve the integral,
I = ∫ 0 π 2 ( sin 2 x ) sin x d x = 1 4 ∫ 0 π 2 ( 3 sin x − sin 3 x ) d x = 1 4 ( 3 ∫ 0 π 2 sin x d x − ∫ 0 π 2 sin 3 x d x )
Evaluate the limits,
I = 1 4 ( [ − 3 cos x ] 0 π 2 + [ cos 3 x 3 ] 0 π 2 ) = 1 4 ( − 3 cos π 2 + 3 cos 0 + 1 3 [ cos 3 π 2 − cos 0 ] ) = 1 4 ( 3 − 1 3 ) = 2 3
Hence, the given result is proved.
The given integral is,
Solve the integral,
Evaluate the limits,
Hence, the given result is proved.
