Question:

If $\int\limits_0^1\left(x^{21}+x^{14}+x^7\right)\left(2 x^{14}+3 x^7+6\right)^{1 / 7} d x=\frac{1}{l}(11)^{m / n}$ where $l, m, n \in N , m$ and $n$ are coprime then $l+m+n$ is equal to ______

Updated On: Sep 24, 2024
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Correct Answer: 63

Solution and Explanation

The correct answer is 63.






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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
  • The area between two curves and the area under a curve
  • 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