Question:
The area bounded by $y =x^{2} +3$ and $y =2x+3$ is
The area bounded by $y =x^{2} +3$ and $y =2x+3$ is
Updated On: Jun 7, 2024
- $\frac{12}{7}$
- $\frac{4}{3}$
- $\frac{3}{4}$
- $\frac{8}{3}$
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The Correct Option is B
Solution and Explanation
Required area
$=\int_{0}^{2}(2 x+3)-\left(x^{2}+3\right) d x$
$=\int_{0}^{2}\left(2 x-x^{2}\right) d x$
$=\left[\frac{2 x^{2}}{2}-\frac{x^{3}}{3}\right]_{0}^{2}$
$=\left[4-\frac{8}{3}\right]=\frac{4}{3}$ sq units
$=\int_{0}^{2}(2 x+3)-\left(x^{2}+3\right) d x$
$=\int_{0}^{2}\left(2 x-x^{2}\right) d x$
$=\left[\frac{2 x^{2}}{2}-\frac{x^{3}}{3}\right]_{0}^{2}$
$=\left[4-\frac{8}{3}\right]=\frac{4}{3}$ 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
- 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