Question

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

Answer 1

The area in the first quadrant bounded by y=4x2,x=0,y=1,and y=4 is

represented by the shaded area ABCDA as

∴Area ABCD=

$\int_{1}^{4} x \,dx$

=

$\int_{1}^{4} \frac{\sqrt y}{2} \,dx$

=$\frac 12$[$\frac{y^{\frac{3}{2}}}{\frac32}$]41

=$\frac 13$[(4)3/2-1]

=$\frac 13$[8-1]

=$\frac 73$units