Question

Find the area of the region lying in the first quadrant and bounded by y = 4 x², x = 0, y = 1 and y = 4.

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Solution

The equation of parabola is

straight y space equals space 4 space straight x squared space space space or space space straight x squared space equals space 1 fourth straight y comma space space

which is upward parabola. The shape of

straight x squared space equals space 1 fourth straight y comma space space straight x space greater or equal than 0 space

is shown in the figure.
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Required area ABCD =

integral subscript 1 superscript 4 straight x space dy space equals space 1 half integral subscript 1 superscript 4 square root of straight y space dy

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