Area can be!

Calculus Level 3

Find the area of closed region bounded by the curves
y = x 2 y=x^2 and y = 1 2 − x 2 y=\dfrac{1}{2-x^2}

Give your answer to 2 decimals

Not Original


The answer is 0.5795.

Prakhar Bindal by Prakhar Bindal , 22, India

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2 solutions

Hana Wehbi
Jun 12, 2016

Area between y = x 2 y=x^{2} and 1 2 − x 2 \frac{1}{2-x^{2}} can be achieved using the following steps:

First we can find the boundaries by equating x 2 = 1 2 − x 2 x^{2}= \frac{1}{2-x^{2}} and solving for x ⟹ x = − 1 o r 1 x \implies x=-1\ or 1 ,

then the area is calculated by taking this integral ∫ − 1 1 ( 1 2 − x 2 − x 2 ) d x \int_{-1}^{1} (\frac{1}{2-x^{2}}-x^{2})dx = ∫ \large\int (Top curve - Bottom curve)

= 2 t a n h − 1 ( 1 2 ) \sqrt{2} tanh^{-1}(\frac{1}{\sqrt{2}}) - 2 3 \frac{2}{3} = 0.579784 0.579784

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Nice Solution! .

Prakhar Bindal - 5 years ago

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Thank you :)

Hana Wehbi - 5 years ago
Vineet Golcha
Jun 12, 2016

U forgot to mention that this problem is not original :-)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Looks good :P right?

Prakhar Bindal - 5 years ago

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