Question:

Find the area bounded by the curve $x = 2 - y - y^2$ and y-axis.

Updated On: Jul 6, 2022
  • $-\frac{9}{2}$
  • $\frac{9}{2}$
  • $9$
  • $-9$
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is B

Solution and Explanation

Put $2 - y - y^2 = 0$ $\Rightarrow y = 1, - 2$ This means, the curve intersects the y-axis at $y = 1$ and $y = - 2$. Hence required area $= \int\limits^{1}_{-2} xdy$ $= \int\limits^{1}_{-2} \left(2-y-y^{2}\right)dy$
$= \left[2y-\frac{y^{2}}{2}-\frac{y^{3}}{3}\right]^{1}_{-2} = \frac{9}{2}$ s units
Was this answer helpful?
0
0

Top Questions on applications of integrals

View More Questions

Notes on applications of integrals

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