Question

what is the answer of following question?

Answer 1

guess we need to solve for b first

Answer 2

\[\int_0^bxdx=\frac{b^2}{2}\]
\[\int_0^bx^2=\frac{b^3}{3}\] solve
\[\frac{b^2}{2}=\frac{b^3}{3}\]

Answer 3

\[b=\frac{3}{2}\] so it should be good from there. you want
\[\int_1^{1.5}(x^2-x )dx\]

Answer 4

If you don't understand the lower limit of the above integration, it's just the point of intersection of y=x^2 and y= x.

Answer 5

\(x^2-x= 0 \implies x=0 \; or \; x=1\)

Now to find the area of the shaded portion we have consider x=1.