Arts (English Medium) इयत्ता १२ - CBSE Important Questions for Mathematics

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)`

Using integration, find the area of the region bounded by the triangle whose vertices are (−1, 2), (1, 5) and (3, 4).

Using integration, find the area of region bounded by the triangle whose vertices are (–2, 1), (0, 4) and (2, 3).

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