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  • Find the area bounded by curves {(x, y) : y ≥ x2 and y = |x|}.

Q : 12         Find the area bounded by curves  \small \left \{ (x,y);y\geq x^2\hspace{1mm} and \hspace{1mm}y=|x| \right \}.

Answers (1)

best_answer

AOI graph

We have to find the area of the shaded region

In the first quadrant

y=|x|=x

Area of the shaded region=2ar(OADO)

\\=2\int_{0}^{1}(x-x^{2})dx\\ =2[\frac{x^{2}}{2}-\frac{x^{3}}{3}]{_{0}}^{1} \\=2(\frac{1}{2}-\frac{1}{3})-0\\ =1-\frac{2}{3}\\ =\frac{1}{3}\ units

The area bounded by the curves is 1/3 units.

Posted by

Sayak

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