List of top Mathematics Questions on Some Properties of Definite Integrals asked in MHT CET

If \(\int _{-π/2}^{π/2}(sin^2x+sin^3x)dx = k\), then the value of \(k\)

If \(\int _0^2x(2-x)^b\,dx = \frac{32}{7}\), where \(b\in N\) then \(b =\)

The value of \(\int _0^π\frac{1}{1+2^{cosx}}\,dx\) is _____

The value of \(\int _{-π}^π\frac{2x(1+sinx)}{1+cos^2x}dx\) is...

\(\int _{π/6}^{π/3}\frac{sinx-cosx}{1+sinxcosx}\,dx =\)

If \(f(x)\) is an even function, then \(\int _{-2}^2(|x|+f(x)sinx)\,\text{d}x\) is

The value of the integral \(\int _{-π/2}^{π/2}(\frac{x^2cosx}{1+e^x})dx\) is equal to \((\frac{π^2}{A})-B\). Then \((\frac{A}{B}) =\)

If \(\int _{π/6}^{π/3}\frac{1}{1+sinx+cosx}dx = log2\), then the value of \(\int _{π/6}^{π/3}\frac{cosx}{1+sinx+cosx}dx =\) ............

The value of the integral \(\int _{-\sqrt{3}}^{\sqrt{3}}\frac{(2x^9+3x^8-5x^7+9x^6+4x^3-x+3)}{x^2+3}\,dx\) is

If \(\int _0^k\frac{1}{1+4^x}dx = log_2(\frac{4}{3})\), then \(k =\) _____

Evaluate the definite integral: \( \displaystyle \int_{0}^{\pi/2} \frac{\sin^n x}{\sin^n x + \cos^n x}\, dx \).

Evaluate the integral: \[ \int_{0}^{\frac{\pi}{2}} \frac{dx}{1+(\cot x)^{101}} \]

If \( 0 \le \cos^{-1} x \le \pi \) and \( -\frac{\pi}{2} \le \sin^{-1} x \le \frac{\pi}{2} \), then at \( x = \frac{1}{5} \) the value of \( \cos(2 \cos^{-1} x + \sin^{-1} x) \) is

The volume of the tetrahedron whose co-terminus edges are $\bar{a}, \bar{b}, \bar{c}$ is 12 cubic units. If the scalar projection of $\bar{a}$ on $\bar{b} \times \bar{c}$ is 4 , then $|\bar{b} \times \bar{c}| =$

The distance of the point $(-3, 2, 3)$ from the line passing through $(4, 6, -2)$ and having direction ratios $-1, 2, 3$ is ________ units.

The normal to the curve $x = 9(1 + \cos \theta), y = 9 \sin \theta$ at $\theta$ always passes through the fixed point}

Evaluate the integral: $\int_0^{\pi / 2} \frac{\cos x}{3 \cos x + \sin x} dx$

Evaluate the integral: $\int_{0}^{1} |5x - 3| dx$

Evaluate the definite integral $$\int_{1}^{3} \left[ \tan^{-1}\left(\frac{x}{x^2-1}\right) + \tan^{-1}\left(\frac{x^2-1}{x}\right) \right] dx$$

$\int_{0}^{\pi / 2} \log\left(\frac{4+3\sin x}{4+3\cos x}\right) dx = $

$\int_0^{\frac{\pi}{2}} \frac{\sin x-\cos x}{1-\sin x \cos x} d x=$

Evaluate the definite integral: $$\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\cos x}{1 + e^x}\ dx$$

If $\int_2^e \left[ \frac{1}{\log x} - \frac{1}{(\log x)^2} \right] dx = a + \frac{b}{\log 2}$, then

If $2 f(x) - 3 f\left(\frac{1}{x}\right) = x$, then $\int_1^e f(x) dx =$

$\int_0^{\frac{\pi}{2}} \frac{\sin x-\cos x}{1-\sin x \cos x} d x=$