Question:
The area enclosed by \(y = |x-1| + |x-2|\) and \(y = 3\)
The area enclosed by \(y = |x-1| + |x-2|\) and \(y = 3\)
Updated On: Mar 21, 2025
Hide Solution
Verified By Collegedunia
Correct Answer: 4
Solution and Explanation
The given equation for \(y\) is \(y = |x - 1| + |x - 2|\). The graph of \(y\)intersects the line \(y = 3\) at certain points, forming a bounded area.
The area can be calculated by finding the points of intersection of the curves and calculating the area between them. After calculating, we find the area is 4 square units.
Was this answer helpful?
0
2
Top Questions on applications of integrals
- Let \[ f(x)=\int \frac{1-\sin(\ell n t)}{1-\cos(\ell n t)} \, dt \] and \[ f\left(e^{\pi/2}\right)=-e^{\pi/2} \] then find $f\left(e^{\pi/4}\right)$.
- JEE Main - 2026
- Mathematics
- applications of integrals
- $A_1$ is the area bounded by $y=x^2+2$, $x+y=8$, and the $y$-axis in the first quadrant, and $A_2$ is the area bounded by $y=x^2+2$, $y^2=x$, $x=0$ and $x=2$ in the first quadrant. Find $(A_1-A_2)$.
- JEE Main - 2026
- Mathematics
- applications of integrals
- If \( \mathbf{F} = ax \hat{i} + by \hat{j} + cz \hat{k} \), where \( a, b, c \) are constants, then
- AP PGECET - 2024
- Engineering Mathematics
- applications of integrals
- The work done in displacing a particle from \( r = 0 \) to \( r = 1 \) in a curve \( x = t^2 + 1 \) and \( z = t^2 + 1 \) in a force field \( \mathbf{F} = (2xy, 3x, -5z) \) is
- AP PGECET - 2024
- Engineering Mathematics
- applications of integrals
- The solution of \( \frac{dy}{\cos y} = dx \) is:
- KEAM - 2024
- Mathematics
- applications of integrals
View More Questions
Questions Asked in JEE Main exam
- When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is \(3.2\ \text{V}\). If a second light having wavelength twice of the first light is used, the stopping potential drops to \(0.7\ \text{V}\). The wavelength of the first light is ________ m.
- JEE Main - 2026
- Photoelectric Effect
- An infinitely long straight wire carrying current $I$ is bent in a planar shape as shown in the diagram. The radius of the circular part is $r$. The magnetic field at the centre $O$ of the circular loop is :
- JEE Main - 2026
- Current electricity
- Identify the correct statements: The presence of –NO\(_2\) group in benzene ring A. activates the ring towards electrophilic substitutions. B. deactivates the ring towards electrophilic substitutions. C. activates the ring towards nucleophilic substitutions. D. deactivates the ring towards nucleophilic substitutions. Choose the correct answer from the options given below:
- JEE Main - 2026
- General Chemistry
- If the distances of the point \( (1,2,a) \) from the line \[ \frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1} \] along the lines \[ L_1:\ \frac{x-1}{3}=\frac{y-2}{4}=\frac{z-a}{b} \quad \text{and} \quad L_2:\ \frac{x-1}{1}=\frac{y-2}{4}=\frac{z-a}{c} \] are equal, then \( a+b+c \) is equal to:
- JEE Main - 2026
- Three Dimensional Geometry
Two circular discs of radius \(10\) cm each are joined at their centres by a rod, as shown in the figure. The length of the rod is \(30\) cm and its mass is \(600\) g. The mass of each disc is also \(600\) g. If the applied torque between the two discs is \(43\times10^{-7}\) dyne·cm, then the angular acceleration of the system about the given axis \(AB\) is ________ rad s\(^{-2}\).
- JEE Main - 2026
- Rotational motion
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:
- 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:
Read More: Area under the curve formula