List of top Mathematics Questions on Integral Calculus

If $k \int_{0}^{1} x f(3x) dx = \int_{0}^{3} t f(t) dt$ then $k =$

$\int_{0}^{2} \frac{dx}{\sqrt{2+x} + \sqrt{2-x}} =$

$\int_{a}^{b} (|x-a| + |x-b|) dx = , (0 < a < b)$

If $\int \frac{1}{(x+100)\sqrt{x+99}} dx = f(x) + c$ then $f(x) =$

$\int (x+1)^{2} e^{x} dx =$

If $\int \frac{2x^{2}+a^{2}}{x^{2}(x^{2}+a^{2})} dx = \frac{k}{x} + \frac{1}{a} \tan^{-1} \frac{x}{a} + c$ then $k =$

$\int \frac{1+\cos 4x}{\cot x - \tan x} dx =$

If $I_{n} = \int \frac{t^{n}}{1+t^{2}} dt$ then $I_{6} + I_{4} =$

$\int \frac{dx}{\sqrt{16-25x^{2}}} =$

$\int_{-\pi/6}^{\pi/6} \frac{\sin^{5}x \cos^{3}x}{x^{4}} dx =$

$\int_{0}^{1} x\sqrt{x^{2}+4} dx =$

$\int_{0}^{\pi/2} \frac{\sin^{100}x}{\sin^{100}x + \cos^{100}x} dx =$

The integral of $f(x) = 1 + x^{2} + x^{4}$ with respect to $x^{2}$ is

If $\int \frac{\sin^{3}x + \cos^{3}x}{\sin^{2}x \cos^{2}x} dx = A\sec x + B\csc x + c$ then $(A, B)$ are}

$\int \frac{dx}{\sqrt{x+1} + \sqrt{x}} =$

$\int \frac{dx}{\sin^{2}x \cos^{2}x} =$

The value of the integral $\int_0^\infty \frac{\log_e (x)}{x^2 + 4} dx$ is:

The area under the curve \[ f(x)=x^5e^{x^3} \] between \(x=1\) and \(x=2\) is

If \[ \alpha=\int_{0}^{2\sqrt{3}} \log_2(x^2+4)\,dx + \int_{2}^{4} \sqrt{2^x-4}\,dx, \] then \(\alpha^2\) is equal to _____.

The area of the region in the first quadrant that is bounded by the parabola

The bounded region enclosed by the curve \(y=x^2+2\) and the line \(y=4x-1\) is revolved about the \(x\)-axis to generate a solid. The volume of the generated solid equals

Let

The double integral of \( f(x,y)=x \) over the triangular region with vertices at \( \left(-\frac{1}{2},\frac{1}{2}\right) \), \( (1,2) \), and \( (1,-1) \) is rounded off to one decimal place.

The volume of the tetrahedron bounded by the planes \(x=1\), \(y=2\), \(z=3\) and \(12x+8y+6z=70\) is rounded off to one decimal place.

\[ \int_0^3 \left(|x-1|-x[x]\right)dx = \underline{} \] rounded off to one decimal place.