Question:

Area bounded by $y = x^3, y = 8$ and $x = 0 $ is

Updated On: May 14, 2024
  • $11 $ s units
  • $14$ s units
  • $12$ s units
  • $6$ s units
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The Correct Option is C

Solution and Explanation

Required area $=\int_{0}^{8} x \,d y $ $=\int_{0}^{8} y^{1 / 3} d y $ $=\frac{3}{4}\left[y^{4 / 3}\right]_{0}^{8}=\frac{3}{4}\left(8^{4 / 3}\right) $ $=\frac{3}{4} \times 16=12$ sq units
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Concepts Used:

Applications of Integrals

There are distinct applications of integrals, out of which some are as follows:

In Maths

Integrals are used to find:

  • The center of mass (centroid) of an area having curved sides
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  • The curve's average value

In Physics

Integrals are used to find:

  • Centre of gravity
  • Mass and momentum of inertia of vehicles, satellites, and a tower
  • The center of mass
  • The velocity and the trajectory of a satellite at the time of placing it in orbit
  • Thrust