The correct evaluation of -0-sin 4 x - dx is -MP PET 1993-A- 8 -3B- 3 -8C- 2 -3D- 4 -3

The correct option is B ∫_0^π|sin^4 x|dx =2 ∫_0^π/2 sin^4 x dx Applying gamma function, 2 ∫_0^π/2sin^4 x dx=2T ( 5/2 ).T ( 1/2 )/2.T ( 6/2 ) =3π/8 ...

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Standard XII

Mathematics

Second Fundamental Theorem of Calculus

The correct e...

Question

The correct evaluation of $\int_{0}^{π} | s i n^{4} x | d x$ is [MP PET 1993]

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Solution

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

The correct option is D ∫π0|sin4 x|dx=2∫π20 sin4 x dx Applying gamma function, 2∫π20sin4 x dx=2T(52).T(12)2.T(62)=3π8

The correct evaluation of $\int_{0}^{π} | s i n^{4} x | d x$ is [MP PET 1993]

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