Question

${\int }_1^2{x}^{2}dx$

• A. $\frac{7}{3}$
• B. $\frac{5}{3}$
• C. $\frac{8}{3}$
• D. $\frac{1}{3}$

Answer 1

The correct option is A $\frac{7}{3}$

With the help of second fundamental theorem we know -
If f(x) is a continuous function defined on [a,b]
${\int }_a^{b}f\left(x\right)dx=F\left(b\right)-F\left(a\right);where{F}^{\prime }\left(x\right)=f\left(x\right)$
So, Using second fundamental theorem we can write -
${\int }_1^2{x}^{2}dx=\frac{(2{)}^3}{3}-\frac{(1{)}^3}{3}$ ; We know $\int x^{2}dx=\frac{(x{)}^3}{3}$
$=\frac{7}{3}$