Science (English Medium) इयत्ता १२ - CBSE Important Questions

Evaluate: `int_((-π)/2)^(π/2) (sin|x| + cos|x|)dx`

Evaluate `int_-1^1 |x^4 - x|dx`.

Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.

Find `int e^x ((1 - sinx)/(1 - cosx))dx`.

If `int_0^(2π) cos^2 x  dx = k int_0^(π/2) cos^2 x  dx`, then the value of k is ______.

Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.

Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.

If `d/dx f(x) = 2x + 3/x` and f(1) = 1, then f(x) is ______.

Find: `int x^4/((x - 1)(x^2 + 1))dx`.

The value of `int_0^(π/4) (sin 2x)dx` is ______.

Evaluate: `int_(-π//4)^(π//4) (cos 2x)/(1 + cos 2x)dx`.

Find: `int e^(x^2) (x^5 + 2x^3)dx`.

Evaluate: `int_0^π x/(1 + sinx)dx`.

For any integer n, the value of `int_-π^π e^(cos^2x) sin^3 (2n + 1)x  dx` is ______.

Evaluate : `int_-1^1 log ((2 - x)/(2 + x))dx`.

Find : `int (2x^2 + 3)/(x^2(x^2 + 9))dx; x ≠ 0`.

Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.

Evaluate: `int_0^(π/4) log(1 + tanx)dx`.

Find the area of the region. 

{(x,y) : 0 ≤ y ≤ x² , 0 ≤ y ≤ x + 2 ,-1 ≤ x ≤ 3} .

Using integration find the area of the triangle formed by negative x-axis and tangent and normal to the circle `"x"^2 + "y"^2 = 9  "at" (-1,2sqrt2)`.