Question:
The area of the region
$A = [(x, y): 0 \leq y \leq x|x|+1$ and $-1 \leq x \leq 1]$ in s units is :
The area of the region
$A = [(x, y): 0 \leq y \leq x|x|+1$ and $-1 \leq x \leq 1]$ in s units is :
Updated On: Apr 28, 2025
- $\frac{2}{3}$
- $\frac{1}{3}$
- 2
- $\frac{4}{3}$
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The Correct Option is C
Solution and Explanation
The graph is a follows
$\int^{0}_{-1} \left(-x^{2} +1\right)dx + \int^{1}_{0} \left(x^{2} +1\right)dx = 2 $
$\int^{0}_{-1} \left(-x^{2} +1\right)dx + \int^{1}_{0} \left(x^{2} +1\right)dx = 2 $
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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