1.

Find the area of the region lying in the first quadrant and bounded by y=4x^2, x=0,y=1 and y=4.

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Solution :The REQUIRED AREA `=overset5underset1intxdy`

`=overset4underset1intsqrty/2 DY(y=4x^2rArrx^2=y/4rArrx=sqrty/2)`
`1/2[y^(3//2)/(3//2)]_1^4=1/3[4^(3//2)-1^(3//2)]`
`=1/3[2^3-1]=7/3`sq.units


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