Can you evaluate the exact form of this definite integral?

Calculus Level 2

Find the exact form of the following definite integral: ∫ 0 1 ( 1 − x 2 / 3 ) 3 / 2 d x . \int_0^1 (1-x^{2/3})^{3/2} \,\mathrm dx.

3 π 31 \dfrac{3\pi}{31} 3 π 33 \dfrac{3\pi}{33} 3 π 32 \dfrac{3\pi}{32} 3 π 30 \dfrac{3\pi}{30}

حكيم الفيلسوف الضائع by حكيم الفيلسوف الضائع , 35, Morocco

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1 solution

Ram Jaiswal
Jan 6, 2017

let x = sin^3 t then function reduces to 3 sin^2t . cos^4t dt after then integrate by Walli's formula

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