Question:
The area of the region bounded by the curves \( y = |x - 2| \), \( x = 1 \), \( x = 3 \) and the x-axis is
The area of the region bounded by the curves \( y = |x - 2| \), \( x = 1 \), \( x = 3 \) and the x-axis is
Show Hint
Always split modulus functions at the point where expression becomes zero.
Updated On: Apr 22, 2026
- 1 sq unit
- 2 sq units
- 3 sq units
- 4 sq units
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Concept:
\[
y = |x-2|
\]
Graph is V-shaped with vertex at \(x=2\).
Step 1: Split interval.
From \(x=1\) to \(2\): \(y = 2 - x\)
From \(x=2\) to \(3\): \(y = x - 2\)
Step 2: Compute area.
\[ \int_1^2 (2-x)\,dx = \frac{1}{2} \] \[ \int_2^3 (x-2)\,dx = \frac{1}{2} \]
Step 3: Total area.
\[ = \frac{1}{2} + \frac{1}{2} = 1 \]
Step 1: Split interval.
From \(x=1\) to \(2\): \(y = 2 - x\)
From \(x=2\) to \(3\): \(y = x - 2\)
Step 2: Compute area.
\[ \int_1^2 (2-x)\,dx = \frac{1}{2} \] \[ \int_2^3 (x-2)\,dx = \frac{1}{2} \]
Step 3: Total area.
\[ = \frac{1}{2} + \frac{1}{2} = 1 \]
Was this answer helpful?
0
0
Top MET Mathematics Questions
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- The equation $3^{3x + 4} = 9^{2x - 2},\ x>0$ has the solution
- A parallelogram is constructed on the vectors $\mathbf{a} = 3\alpha - \beta$, $\mathbf{b} = \alpha + 3\beta$. If $|\alpha| = |\beta| = 2$ and the angle between $\alpha$ and $\beta$ is $\dfrac{\pi}{3}$, then the length of a diagonal of the parallelogram is
- Every group of order 7 is
- Let $U_{n} = 2 + 2^{3} + 2^{5} + \cdots + 2^{2n+1}$ and $V_{n} = 1 + 4 + 4^{2} + \cdots + 4^{n-1}$. Then $\displaystyle\lim_{n \to \infty} \dfrac{U_n}{V_n}$ is equal to
View More Questions
Top MET Area under Simple Curves Questions
- The area bounded by the curve $y = \sin x$ between $x = 0$ and $x = \pi$ is:
- The area bounded by the parabola $y^{2 = 4ax$ and its latus rectum is:
- The area of the region bounded by the curve \( x = 4 - y^{2} \) and the y-axis is:
- The area of the region bounded by the curve \( x = 4 - y^{2} \) and the y-axis is:
- The line \( x = \frac{\pi}{4} \) divides the area of the region bounded by \( y = \sin x \), \( y = \cos x \) and the x-axis \( (0 \le x \le \frac{\pi}{2}) \) into areas \( A_{1} \) and \( A_{2} \). Then \( A_{1} : A_{2} \) equals
View More Questions
Top MET Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- Which of the following product is formed in the reaction $ CH_3MgBr {->[(i)CO_2][(ii)H_2O]} ? $
View More Questions