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

\[\int\limits_{- \pi}^\pi x^{10} \sin^7 x dx\]

\[\int\limits_0^1 \cot^{- 1} \left( 1 - x + x^2 \right) dx\]

\[\int\limits_0^\pi \frac{dx}{6 - \cos x}dx\]

\[\int\limits_0^{\pi/2} \frac{1}{2 \cos x + 4 \sin x} dx\]

\[\int\limits_{\pi/6}^{\pi/2} \frac{\ cosec x \cot x}{1 + {cosec}^2 x} dx\]

\[\int\limits_0^{\pi/2} \frac{dx}{4 \cos x + 2 \sin x}dx\]

\[\int\limits_0^4 x dx\]

\[\int\limits_0^2 \left( 2 x^2 + 3 \right) dx\]

\[\int\limits_1^4 \left( x^2 + x \right) dx\]

\[\int\limits_{- 1}^1 e^{2x} dx\]

\[\int\limits_2^3 e^{- x} dx\]

\[\int\limits_1^3 \left( 2 x^2 + 5x \right) dx\]

\[\int\limits_1^3 \left( x^2 + 3x \right) dx\]

\[\int\limits_0^2 \left( x^2 + 2 \right) dx\]

\[\int\limits_0^3 \left( x^2 + 1 \right) dx\]

Find : `∫_a^b logx/x` dx

Prove that `int_a^b ƒ ("x") d"x" = int_a^bƒ(a + b - "x") d"x" and "hence evaluate" int_(π/6)^(π/3) (d"x")/(1+sqrt(tan "x")`

If A is 3 × 3 invertible matrix, then show that for any scalar k (non-zero), kA is invertible and `("kA")^-1 = 1/"k" "A"^-1`

Find inverse, by elementary row operations (if possible), of the following matrices

`[(1, 3),(-5, 7)]`

Find inverse, by elementary row operations (if possible), of the following matrices

`[(1, -3),(-2, 6)]`