List of top Mathematics Questions on Integration asked in KEAM

The coefficient of \( x^7 \) in the expansion of \( \left( \frac{1}{x + x^2} \right)^8 \) is
The value of \( \int_{-1}^{1} x^2 \sin x \, dx \) is equal to:
The order and degree of the following differential equation: \( \frac{d^2 y}{dx^2} - 2x = \sqrt{y} + \frac{dy}{dx} \), respectively, are:
The common ratio of a G.P. is 10. Then the ratio between its 11th term and its 6th term is:
If \( P(-3, 4) \) and \( Q(3, 1) \) are points on a straight line, then the slope of the straight line perpendicular to PQ is:
The length of perpendicular from the origin to the line \( \frac{x}{5} - \frac{y}{12} = 1 \) is:
The equation of the straight line passing through the point \( (1, 1) \) and perpendicular to the line \( x + y = 5 \) is:
The area of the triangle formed by the coordinate axes and a line whose perpendicular from the origin makes an angle of 45° with the x-axis is 50 square units. Then the equation of the line is:
The equation of the straight line, intersecting the coordinate axes \( x \) and \( y \) are respectively 1 and 2, is:
If the sum of distances of a point from the origin and the line \( x = 3 \) is 8, then its locus is:
A line makes angles \( \alpha, \beta, \gamma \) with \( x, y \), and \( z \)-axes respectively. Then the value of \( \sin^2\alpha + \sin^2\beta - \cos^2\gamma \) is:
The direction ratios of the line joining the points \( (2, 3, 4) \) and \( (-1, 4, -3) \) is:
Evaluate the integral \[ \int \frac{e^x}{2^x} dx. \]
Evaluate the integral \[ \int x^5 e^{x^3} \,dx. \]
Let \(f:\R\rightarrow\R\) be defined by
\(f(x) =   \begin{cases} x & \text{if}\ x\leq1 \\  -x+2 & \text{if}\ x\gt1\end{cases}\)
Then \(\int^{2}_{0}f(x)dx=\)
\(\int\frac{2\tan x+3}{\sin^2x+2\cos^2x}dx=\)
\(\int\frac{1}{x^2-2x+2}dx=\)
\(\int^{1}_{0}\frac{2e^x}{1+e^{2x}}dx=\)
The value of \(\displaystyle\int^{\frac{\pi}{16}}_{0}\cos6x\cos2xdx\) is equal to
The value of \(\displaystyle\int^{10}_{-10}\frac{x^{10}\sin x}{\sqrt{1+x^{10}}}dx\) is equal to
The value of \(\int^{2}_{-1}(x-2)|x|)dx\) is equal to
The value of \(\displaystyle\int^{\frac{\pi}{2}}_{\frac{\pi}{6}}\frac{\cot x}{\sin x}dx \) is equal to
\(\int\frac{dx}{x^2-x}=\)
\(\int\sin^3xdx+\int\cos^2x\sin xdx=\)
\(\int(\tan^2(2x)-\cot^2(2x))dx=\)