Question

Which of the following integral represents the summation ${\sum }^{}\left(4x^3\right)\delta x$ for the limit $\delta x\to 0$?

• A.
  $\int \left(4x\right)dx$
• B.
  $\int \left(4x^2\right)$
• C.
  $\int \left(4x^3\right)dx$
• D.
  $\int \left(4x^4\right)dx$

Answer 1

The correct option is C

$\int \left(4x^3\right)dx$
As the limit $\delta x\mathrm{tends}\mathrm{to}0$, $\delta x$ is now differential $dx$ while the integrand is $4x^3$.
So, we write the integral as $I=\int \left(4x^3\right)dx$.