Question

Figure shows the curve $y=x^2$.Find the area of the shaded part between $x=0$ and $x=6$

• A. $216uni{t}^2$
• B. $72uni{t}^2$
• C. $12uni{t}^2$
• D. None of these

Answer 1

The correct option is B

$72uni{t}^2$

The area can be divided into strips by drawing ordinates between x = 0 and x = 6 at a regular interval of dx. Consider the strip between the ordinates at x and x + dx. The height of this strip is $y=x^2$. The area of this strip is dA = y dx = $x^{2}dx$.

The total area of the shaded part is obtained by summing up these strip-areas with x varying from 0 to 6. Thus

$A=\underset{0}{\overset{6}{\int }}{x}^{2}dx$

=$[\frac{x^3}{3}{]}_0^6=\frac{216-0}{3}=72$