Question:
The area bounded by $y =x^{2} +3$ and $y =2x+3$ is
The area bounded by $y =x^{2} +3$ and $y =2x+3$ is
Updated On: Apr 8, 2026
- $\frac{12}{7}$
- $\frac{4}{3}$
- $\frac{3}{4}$
- $\frac{8}{3}$
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Required area
$=\int_{0}^{2}(2 x+3)-\left(x^{2}+3\right) d x$
$=\int_{0}^{2}\left(2 x-x^{2}\right) d x$
$=\left[\frac{2 x^{2}}{2}-\frac{x^{3}}{3}\right]_{0}^{2}$
$=\left[4-\frac{8}{3}\right]=\frac{4}{3}$ sq units
$=\int_{0}^{2}(2 x+3)-\left(x^{2}+3\right) d x$
$=\int_{0}^{2}\left(2 x-x^{2}\right) d x$
$=\left[\frac{2 x^{2}}{2}-\frac{x^{3}}{3}\right]_{0}^{2}$
$=\left[4-\frac{8}{3}\right]=\frac{4}{3}$ sq units
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM applications of integrals Questions
- The set $\{(x, y) : x + y =1\}$ in the $xy$ plane represents
- The area bounded by the curves $y = - x^2 + 3$ and $y = 0$ is
- The area bounded by the curve y = x(2-x) and the line y=x is
- The solution of \( \frac{e^y}{dx} = x + 2 \) is:
- The solution of \( \frac{dy}{\cos y} = dx \) is:
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions
Concepts Used:
Applications of Integrals
There are distinct applications of integrals, out of which some are as follows:
In Maths
Integrals are used to find:
- The center of mass (centroid) of an area having curved sides
- The area between two curves and the area under a curve
- The curve's average value
In Physics
Integrals are used to find:
- Centre of gravity
- Mass and momentum of inertia of vehicles, satellites, and a tower
- The center of mass
- The velocity and the trajectory of a satellite at the time of placing it in orbit
- Thrust