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
- 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 \( \frac{e^y}{dx} = x + 2 \) is:
- KEAM - 2024
- Mathematics
- applications of integrals
- The solution of \( \frac{dy}{\cos y} = dx \) is:
- KEAM - 2024
- Mathematics
- applications of integrals
- Evaluate: \( \int \frac{1}{\sqrt{a^2 - x^2}} \, dx \).
- UP Board XII - 2024
- Mathematics
- applications of integrals
View More Questions
Questions Asked in JEE Main exam
- Three infinitely long wires with linear charge density \( \lambda \) are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface?
- JEE Main - 2025
- electrostatic potential and capacitance
- The number of 6-letter words, with or without meaning, that can be formed using the letters of the word "MATHS" such that any letter that appears in the word must appear at least twice is:
- JEE Main - 2025
- Calculus
- Number of functions \( f: \{1, 2, \dots, 100\} \to \{0, 1\} \), that assign 1 to exactly one of the positive integers less than or equal to 98, is equal to:
- JEE Main - 2025
- Vectors
- Let \( P_n = \alpha^n + \beta^n \), \( P_{10} = 123 \), \( P_9 = 76 \), \( P_8 = 47 \), and \( P_1 = 1 \). The quadratic equation whose roots are \( \frac{1}{\alpha} \) and \( \frac{1}{\beta} \) is:
- JEE Main - 2025
- Sequences and Series
- Suppose that the number of terms in an A.P. is \( 2k, k \in \mathbb{N} \). If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55, and the last term of the A.P. exceeds the first term by 27, then \( k \) is equal to:
- JEE Main - 2025
- Arithmetic Progression
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