A calculus problem by حسن العطية

Calculus Level 2

∫ 0 1 1 − x 2 d x = ? \int _{ 0 }^{ 1 }{ \sqrt { 1-{ x }^{ 2 } } \, dx } = \, ?

π \pi π 4 \frac { \pi }{ 4 } π 2 \frac { \pi }{ 2 } 1

حسن العطية by حسن العطية , 22, Saudi Arabia

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2 solutions

展豪 張
Apr 19, 2016

It is a quarter of area of a unit circle, so the answer is π 4 \dfrac \pi 4

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Indefinite integral

∫ 1 − x 2 d x = 1 2 ( sin ⁡ − 1 ( x ) + 1 2 sin ⁡ ( 2 sin ⁡ − 1 ( x ) ) ) + C \int \sqrt{1-x^2}\,dx = \frac{1}{2}\left(\sin^{-1}(x) + \frac{1}{2}\sin(2\sin^{-1}(x))\right) +C

Boundaries: ∫ 0 1 1 − x 2 d x = π 4 □ \int_{0}^{1}\sqrt{1-x^2}\,dx = \frac{\pi}{4} \square

ADIOS!!! \large \text{ADIOS!!!}

3 Helpful 0 Interesting 0 Brilliant 1 Confused

how is the indefinite part is done? which method?

Faraz Khan - 4 years, 3 months ago

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Integration by-parts.

Arghyadeep Chatterjee - 8 months, 3 weeks ago

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