List of top Mathematics Questions on Definite Integral asked in KEAM

The value of $\int_{0}^{3}x^{2}[x]dx$ is equal to
The value of $\int_{-2}^{1}\frac{|x|}{x}dx$ is equal to
The value of $\int_{0}^{\pi}\frac{\sin x}{1+\sin x}dx$ is equal to} \textit{Note: The upper limit in the integral from the original paper contains a typo ($x$ instead of $\pi$). It has been corrected here to yield the valid options provided.
The value of $\displaystyle \int_{0}^{1} x(1-x)^4 \, dx$ is equal to:
$\displaystyle \int_{-6}^{0} \left[t^3 + 9t^2 + 27t + 29 + (t+3)\cos(t+3)\right] dt$ is equal to:
If $I = \displaystyle \int_{-1}^{1} \frac{x^4}{1 - x^4} \cos^{-1}\left(\frac{2x}{1+x^2}\right) dx$, then $2I$ is equal to:
$\displaystyle \int_{0}^{1} \left[\tan^{-1}\left(\frac{1}{1+x+x^2+x^3}\right) + \tan^{-1}(1+x+x^2+x^3)\right] dx$ is equal to:
The value of the integral \(\int_{0}^{\pi} \frac{\cos x}{1 + \sin^{2} x} \, dx\) is
\(\int_{0}^{\frac{\pi}{2}} \sin 2x\,e^{\sin x}\,dx\) is equal to
$\int_{0}^{1}\frac{\sin x}{\sin x+\sin(1-x)}\,dx$ is equal to:
$\int_{-2}^{2}|x+3|\,dx =$
$\int_{0}^{\frac{\pi}{2}}\frac{1}{1+\sin x}\,dx =$
\( \int_{0}^{1} \frac{3^{2x}}{3^x + 1}\,dx = \)
The value of \( \int_{\pi/10}^{2\pi/5} \frac{\cot^3 x}{1+\cot^3 x}\,dx \) is equal to
If \( \int_{-\sqrt{3}}^{1} (-6x^2 + 18)\,dx = \alpha + \beta\sqrt{3} \), then the value of \( \alpha + \beta \) is equal to
\(\int_{0}^{2} \frac{x^{4}}{x^{4} + (2 - x)^{4}} \, dx =\)
The value of \(\int_{0}^{\pi/3}\frac{\tan t}{\cos t} dt\) is equal to
The value of \(\int_{-1}^{1}|x - 3|dx\) is equal to

Let

\[ f(x) + 2f\left(\frac{1}{x}\right) = \frac{1}{x} - 5 \] 

Then

\[ \int_{1}^{2} 3f(x)\,dx \]

equals ______.

Let \( f(x) \) be differentiable and 

\[ \int_{0}^{t^2} x f(x)\,dx = \frac{1}{2} t^4 \quad \text{for all } t. \]

Then the value of \( f(17) \) is ______.

The value of the definite integral \( \int_0^{2\pi} \sqrt{1 + \sin \frac{x}{2}}\, dx \) is
The value of the integral \( \int_{0}^{\pi} \frac{\cos x}{1+\sin^2 x} \, dx \) is
\( \int_{\pi/4}^{3\pi/4} \frac{x}{1+\sin x} \, dx \) is equal to
\( \int_{0}^{\pi/2} \frac{2\sin x}{2\sin x + 2\cos x} dx \)
If \( \int_{-1}^{1} f(x)dx = 4 \) and \( \int_{2}^{1} (3-f(x))dx = 7 \), then \( \int_{-1}^{2} f(x)dx \) is