List of top Mathematics Questions on applications of integrals asked in KEAM

Let $f(x) = \frac{1}{20}(x - 5)^2, x \in \mathbb{R}$. If $\int_{-5}^{5} f(x) dx = \int_5^{a} f(x) dx$, where $a > 5$ is a real constant, then the value of $a$ is equal to

Area of the region bounded by the function $f(x)=\begin{cases} x, & x\leq 3 \\ -x+6, & x>3 \end{cases}$ with the $x$-axis (in square units) in the first quadrant is:

The area of the region bounded by \( y = x^{5/2} \) and \( y = x \) (in square units) is

The solution of \( \frac{dy}{\cos y} = dx \) is:

The area bounded by the curve y = x(2-x) and the line y=x is

The area enclosed by the curve $x=3\cos\theta$, $y=2\sin\theta$, $0\le\theta\le\pi$, is (in square units)

The area of the region bounded by $y=|x|$, $y=0$, $x=3$ and $x=-3$ is (in square units)

The area enclosed between the curves \( y = 2x^2 + 1 \) and \( y = x^2 + 5 \) is:

Area bounded by \( y=\sin^2 x \), \( x=\frac{\pi}{2} \), \( x=\pi \)

Area bounded by \( y=\sin^2 x \), \( x=\frac{\pi}{2} \), \( x=\pi \)

The area bounded by the lines $y - 2x = 2$, $y = 4$ and the y-axis is equal to (in square units):

The area bounded by \( y = x^2 + 3 \) and \( y = 2x + 3 \) is (in sq. units)

The set $\{(x, y) : x + y =1\}$ in the $xy$ plane represents

The area bounded by $y =x^{2} +3$ and $y =2x+3$ is

The area bounded by the curves $y = - x^2 + 3$ and $y = 0$ is