Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Application of Integrals

Question:

The area of the region bounded by the curve \(y=x^{3}\) and the line \(y=4\) is

Options:

\(\frac{32}{3}\)

\(\frac{64}{3}\)

\(\frac{256}{3}\)

\(\frac{128}{3}\)

Correct Answer:

\(\frac{32}{3}\)

Explanation:

y → 0

y → 4

area of curve = $\int\limits_0^4y^{\frac{1}{3}}dy=\left[\frac{3y^{\frac{4}{3}}}{4}\right]_0^4$

$=3×4^{\frac{1}{3}}$ sq. units