Dirty Curve, Clean area!

Calculus Level 4

Find the area bounded by curve y 2 = x 3 2 − x y^{2}=\dfrac{x^{3}}{2-x} and the ordinate x = 2 x=2 .


The answer is 9.42.

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Pranjal Jain by Pranjal Jain , 23, India

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1 solution

Pranjal Jain
Dec 8, 2014

Plot of curve Plot of curve

A r e a = 2 × ∫ 0 2 x x 2 − x d x Area=2×\displaystyle\int_{0}^{2} x\sqrt{\dfrac{x}{2-x}} dx

Substitute x = 1 + c o s θ x=1+cos\theta ,

A r e a = 2 × ∫ − π 0 ( 1 + cos ⁡ θ ) 2 d θ Area=2×\displaystyle\int_{-\pi}^{0} (1+\cos \theta)^{2} d\theta

⇒ A r e a = 3 π = 9.42 \Rightarrow Area=3\pi=\boxed{9.42}

9 Helpful 0 Interesting 1 Brilliant 0 Confused

oh!!! I just missed it

madhur trivedi - 4 years, 3 months ago

Integration can also be done using beta function!!

A Former Brilliant Member - 3 years, 8 months ago

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Yup!!! That is what I did........along with converting the curve into Polar co-ordinates.......!!!

Aaghaz Mahajan - 2 years, 11 months ago

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