- - - 0 - -160- - 2 -160- sin - 3 - 2 -160- x -160- -sin - 3 - 2 -160- x -cos - 3 - 2 -160- x -160- -160- dx-4-TrueFalse

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Standard X

Mathematics

Sum of Infinite Terms of a GP

∫ _ 0 ^π #1...

Question

$\int_{0}^{\frac{π}{2}} \frac{{sin}^{\frac{3}{2}} x}{{sin}^{\frac{3}{2}} x + {cos}^{\frac{3}{2}} x} d x = \frac{π}{4}$

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Similar questions

\int_{0}^{\frac{π}{2}} {sin}^{3} x d x = \frac{2}{3}

Q. Evaluate:

\int_{0}^{\frac{π}{2}} {sin}^{3} x d x

\int_{0}^{\frac{π}{4}} \frac{{sin}^{2} x . {cos}^{2} x}{{({sin}^{3} x + {cos}^{3} x)}^{2}} d x = \frac{m}{6}

.Find

m

Q. Consider

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} [\frac{2 (sin x - {sin}^{3} x) + ∣ ∣ sin x - {sin}^{3} x ∣ ∣}{2 (sin x - {sin}^{3} x) - ∣ ∣ sin x - {sin}^{3} x ∣ ∣}], x \neq \frac{π}{2} f o r x \in (0, π) 3 x = \frac{π}{2} \end{matrix}

, where

[]

denotes the greatest integer function, then-

By using properties of definite integrals, evaluate the integrals
$\int_{0}^{\frac{π}{2}} \frac{s i n^{\frac{3}{2}}}{s i n^{\frac{3}{2}} x + c o s^{\frac{3}{2}} x} d x .$

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∫π20sin32xsin32x+cos32xdx=π4

$\int_{0}^{\frac{π}{2}} \frac{{sin}^{\frac{3}{2}} x}{{sin}^{\frac{3}{2}} x + {cos}^{\frac{3}{2}} x} d x = \frac{π}{4}$