Commerce (English Medium) कक्षा १२ - CBSE Important Questions

Evaluate :

`∫(x+2)/sqrt(x^2+5x+6)dx`

Evaluate : `int_2^3 3^x dx`

Find  `int dx/(x^2 + 4x + 8)`

Evaluate `int_0^(3/2) |x sin pix|dx`

Evaluate `int (cos 2x + 2sin^2x)/(cos^2x) dx`

Find `int (2cos x)/((1-sinx)(1+sin^2 x)) dx`

Evaluate `int_0^(pi/4) (sinx + cosx)/(16 + 9sin2x) dx`

Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`

Find: `int (dx)/(x^2 - 6x + 13)`

Evaluate: `int_0^(2π) (1)/(1 + e^(sin x)`dx

Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is ______.

Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.

`int secx/(secx - tanx)dx` equals ______.

Assertion (A): `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x))dx` = 3.

Reason (R): `int_a^b f(x) dx = int_a^b f(a + b - x) dx`.

Evaluate: `int_0^(π/2) sin 2x tan^-1 (sin x) dx`.

Using integration find the area of the region {(x, y) : x2+y2⩽ 2ax, y2⩾ ax, x, y ⩾ 0}.

Using integration find the area of the triangle formed by positive x-axis and tangent and normal of the circle

`x^2+y^2=4 at (1, sqrt3)`

Find the area bounded by the circle x² + y² = 16 and the line `sqrt3 y = x` in the first quadrant, using integration.

Solve the following differential equation: `(x^2-1)dy/dx+2xy=2/(x^2-1)`

Find the particular solution of the differential equation

(1 – y²) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.