Arts (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

The value of \[\int\limits_0^{\pi/2} \cos x\ e^{\sin x}\ dx\] is

If \[\int\limits_0^a \frac{1}{1 + 4 x^2} dx = \frac{\pi}{8},\] then a equals

If \[\int\limits_0^1 f\left( x \right) dx = 1, \int\limits_0^1 xf\left( x \right) dx = a, \int\limits_0^1 x^2 f\left( x \right) dx = a^2 , then \int\limits_0^1 \left( a - x \right)^2 f\left( x \right) dx\] equals

The value of \[\int\limits_{- \pi}^\pi \sin^3 x \cos^2 x\ dx\] is 

The derivative of \[f\left( x \right) = \int\limits_{x^2}^{x^3} \frac{1}{\log_e t} dt, \left( x > 0 \right),\] is

If \[I_{10} = \int\limits_0^{\pi/2} x^{10} \sin x\ dx,\]  then the value of I₁₀ + 90I₈ is

The value of the integral \[\int\limits_{- 2}^2 \left| 1 - x^2 \right| dx\] is ________ .

The value of \[\int\limits_0^\pi \frac{1}{5 + 3 \cos x} dx\] is

\[\int\limits_0^{2a} f\left( x \right) dx\]  is equal to

If f (a + b − x) = f (x), then \[\int\limits_a^b\] x f (x) dx is equal to