The area (in sq. units) of the region enclosed between the parabola y2 = 2x and the line x + y = 4 is _______.
Correct Answer: 18
Solution and Explanation
The correct answer is 18
Required Area :
\(= \int_{-4}^{2} \left(4 - y - \frac{y^2}{2}\right) \,dy\)
\(=\left[4y - \frac{y^2}{2} - \frac{y^3}{6}\right]_{2}^{4}\)
= 18 square units.
Top Questions on Area between Two Curves
If the area of the region $\{ (x, y) : |x - 5| \leq y \leq 4\sqrt{x} \}$ is $A$, then $3A$ is equal to
- JEE Main - 2025
- Mathematics
- Area between Two Curves
- The area of the region enclosed by the curves \( y = x^2 - 4x + 4 \) and \( y^2 = 16 - 8x \) is:
- JEE Main - 2025
- Mathematics
- Area between Two Curves
- Let $A$ be the area of the region
$\left\{(x, y): y \geq x^2, y \geq(1-x)^2, y \leq 2 x(1-x)\right\}$.
Then $540 A$ is equal to ______.- JEE Main - 2025
- Mathematics
- Area between Two Curves
- The area of the region \[ \{ (x, y) : x^2 + 4x + 2 \leq y \leq |x| + 2 \} \] is equal to:
- JEE Main - 2025
- Mathematics
- Area between Two Curves
- If the area of the region $ \{(x, y) : 1 + x^2 \leq y \leq \min(x + 7, 11 - 3x)\} $ is $ A $, then $ 3A $ is equal to:
- JEE Main - 2025
- Mathematics
- Area between Two Curves
Questions Asked in JEE Main exam
Considering Bohr’s atomic model for hydrogen atom :
(A) the energy of H atom in ground state is same as energy of He+ ion in its first excited state.
(B) the energy of H atom in ground state is same as that for Li++ ion in its second excited state.
(C) the energy of H atom in its ground state is same as that of He+ ion for its ground state.
(D) the energy of He+ ion in its first excited state is same as that for Li++ ion in its ground state.- JEE Main - 2025
- Atomic Models
- In an adiabatic process, which of the following statements is true?
- JEE Main - 2025
- Thermodynamics
- To obtain the given truth table, the following logic gate should be placed at G
- JEE Main - 2025
- Logic gates
- Choose the correct logic circuit for the given truth table having inputs A and B.
- JEE Main - 2025
- Logic gates
A slanted object AB is placed on one side of convex lens as shown in the diagram. The image is formed on the opposite side. Angle made by the image with principal axis is:
Concepts Used:
Area between Two Curves
Integral calculus is the method that can be used to calculate the area between two curves that fall in between two intersecting curves. Similarly, we can use integration to find the area under two curves where we know the equation of two curves and their intersection points. In the given image, we have two functions f(x) and g(x) where we need to find the area between these two curves given in the shaded portion.
Area Between Two Curves With Respect to Y is
If f(y) and g(y) are continuous on [c, d] and g(y) < f(y) for all y in [c, d], then,
