Question:

The area bounded by the line $y - x$ , x-axis and lines $x = -1$ to $x = 2$, is

Updated On: Jul 7, 2022
  • $0$ s unit
  • $1/2$ s unit
  • $3/2$ s unit
  • $5/2$ s unit
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is D

Solution and Explanation

We have $y=x$
Required area = area of shaded region $A=\left|\int\limits_{-1}^{0}x dx\right|+\left|\int\limits_{0}^{2}xdx\right|=\left|\frac{x^{2}}{2}\right|_{-1}^{0}+\left|\frac{x^{2}}{2}\right|_{0}^{2}$ $=\left|-\frac{1}{2}\right|+\left|2\right|=2+\frac{1}{2}=\frac{5}{2}$ s units
Was this answer helpful?
0
0

Top Questions on Area under Simple Curves

View More Questions

Concepts Used:

Area under Simple Curves

  • The area of the region bounded by the curve y = f (x), x-axis and the lines x = a and x = b (b > a) - given by the formula:
\[\text{Area}=\int_a^bydx=\int_a^bf(x)dx\]
  • The area of the region bounded by the curve x = φ (y), y-axis and the lines y = c, y = d - given by the formula:
\[\text{Area}=\int_c^dxdy=\int_c^d\phi(y)dy\]

Read More: Area under the curve formula