The correct evaluation of ∫ π 0 | s i n 4 x | d x is [MP PET 1993] Options: A . &nbsp8π3 B . &nbsp2π3 C . &nbsp4π3 D . &nbsp3π8

Answer: Option D : D ∫ π 0 | s i n 4 x | d x = 2 ∫ π 2 0 s i n 4 x d x Applying gamma function, 2 ∫ π 2 0 s i n 4 x d x = 2 T ( 5 2 ) . T ( 1 2 ) 2. T ( 6 2 ) = 3 π 8

The correct evaluation of ∫π0|sin4 x|dx is [MP PET 1993]

Question

The correct evaluation of

\int_{0}^{π} | s i n^{4} x | d x

is [MP PET 1993]

Options:

A . 8π3

B . 2π3

C . 4π3

D . 3π8

Answer: Option D
:
D

\int_{0}^{π} | s i n^{4} x | d x = 2 \int_{0}^{\frac{π}{2}} s i n^{4} x d x

Applying gamma function,

2 \int_{0}^{\frac{π}{2}} s i n^{4} x d x = 2 \frac{T (\frac{5}{2}) . T (\frac{1}{2})}{2. T (\frac{6}{2})} = \frac{3 π}{8}

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