List of top Mathematics Questions on Integration

\( \int (x + 1)(x - x^2) e^x \, dx \) is equal to
If \( f(x) = x - \lfloor x \rfloor \), for every real number \( x \), where \( \lfloor x \rfloor \) is the integral part of \( x \), then \[ \int f(x) \, dx \] is equal to
The value of the integral \[ \int_1^\infty \frac{x+1}{|x-1|} \left( \frac{x-1}{x+1} \right)^{1/2} \, dx \] is
\[ \int \frac{dx}{\sin x - \cos x + \sqrt{2}} = ? \]
The value of the integral \[ I = \int_0^1 \frac{\sqrt{1 - x}}{\sqrt{1 + x}} \, dx \] is:
The value of the integral \[ I = \int_0^1 \left| x - \frac{1}{2} \right| \, dx \] is:
Evaluate \[ \int \frac{x^2 + 4}{x^4 + 16} \, dx \]
Evaluate \[ \int_{ \frac{\pi}{4} }^{ \frac{3\pi}{4} } \frac{1}{1 + \cos x} \, dx \]
If \(\displaystyle \int_{1}^{x}\frac{dt}{t\sqrt{t^2-1}}=\frac{\pi}{6}\), then \(x\) can be equal to
The area bounded by the curve \(y=|\sin x|\), \(x\)-axis and the lines \(x=\pi\), is
If \(\{f(x)\dx=f(x)\), then \(\int \{f(x)\}^2 dx\) is equal to}
\(\displaystyle \int \sin^{-1}\left(\frac{2x+2}{\sqrt{4x^2+8x+13}}\right)dx\) is equal to
The line \(x=\frac{\pi}{4}\) divides the area of the region bounded by \(y=\sin x\), \(y=\cos x\) and x-axis \((0\leq x\leq \frac{\pi}{2})\) into two regions of areas \(A_1\) and \(A_2\). Then \(A_1:A_2\) equals
If
\[ \int \left(\frac{2-\sin2x}{1-\cos2x}\right)e^x\,dx \] is equal to
If \(I_n=\int \sin^n x\,dx\), then \(I_n-nI_{n-2}\) equals
The value of \(\int_{0}^{a}\sqrt{\frac{a-x}{x}}\,dx\) is
If \(I=\int \frac{x^5}{\sqrt{1+x^3}}\,dx\), then \(I\) is equal to
The value of \( \int_0^\infty \frac{dx}{(a^2 + x^2)^7} \) is equal to
The value of the integral \[ \int e^x \left( \frac{1 - x}{1 + x^2} \right)^2 dx \] is
The value of \( \int_{1}^{4} |x - 3| \, dx \) is equal to
The area of the region bounded by the straight lines \( x = 0 \) and \( x = 2 \) and the curves \( y = 2x^2 \) and \( y = 2x - x^2 \) is equal to
If \( f'(x) = \frac{x}{\sqrt{1 + x^2}} \) and \( f(0) = 0 \), then \( f(x) = \):
What is the area of a loop of the curve \( r = a \sin 30^\circ \)?
The value of the integral \( \int_1^4 \sqrt{t} \, dt \) is:
The value of the integral \( \int_0^{\frac{\pi}{2}} \log (\tan x) \, dx \) is: