Question

If$\int f\left(x\right)dx=f\left(x\right)$ , $then\int \left\{f\right(x){\}}^{2}dx$ is equal to

• A. $\frac{1}{2}\left\{f\right(x){\}}^2$
• B. $\left\{f\right(x){\}}^3$
• C. $\frac{|f\left(x\right){|}^3}{3}$
• D. $\left\{f\right(x){\}}^2$

Answer 1

Answer: (A)

$\frac{1}{2}\left\{f\right(x){\}}^2$

$df\left(x\right)=f\left(x\right)\cdot dx\cdot$ .....(1)

from $\int f\left(x\right)dx=f\left(x\right)$

$\int \left(f\right(x){)}^{2}dx$ = $\int f\left(x\right)\cdot f\left(x\right)\cdot dx$

$=\int f\left(x\right)df\left(x\right)$ .....from (1)

$=\frac{1}{2}\left(f\right(x){)}^2+c$

$\int \left\{f\right(x){\}}^{2}dx=\frac{1}{2}\{f\left(x\right){\}}^2+c.$