Area Question 32

Question 32

  1. Find the area bounded by the curves x2=y,x2=y and y2=4x3.

(2005,4 M)

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Solution:

  1. The region bounded by the curves y=x2,y=x2 and y2=4x3 is symmetrical about X-axis, where y=4x3 meets at (1,1).

Area of curve (OABCO)

=201x2dx3/41(4x3)dx

$$ \begin{aligned} & =2{\frac{x^{3}}{3}}{0}^{1}-{\frac{(4 x-3)^{3 / 2}}{3 \cdot 4 / 2}}{3 / 4}^{1} \ & =2 \frac{1}{3}-\frac{1}{6} \ & =1 \cdot \frac{1}{6}=\frac{1}{3} \mathrm{sq} \text { unit } \end{aligned} $$



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