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