Arts (English Medium) कक्षा १२ - CBSE Important Questions

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`.

Using integration, find the area bounded by the curve x² = 4y and the line x = 4y − 2.

Using integration, find the area of the region bounded by the lines y = 2 + x, y = 2 – x and x = 2.

Using the method of integration, find the area of the triangular region whose vertices are (2, -2), (4, 3) and (1, 2).

Sketch the region bounded by the curves `y=sqrt(5-x^2)` and y=|x-1| and find its area using integration.

Sketch the graph y = |x + 1|. Evaluate\[\int\limits_{- 4}^2 \left| x + 1 \right| dx\]. What does the value of this integral represent on the graph?

Using integration find the area of the region bounded by the curves \[y = \sqrt{4 - x^2}, x^2 + y^2 - 4x = 0\] and the x-axis.

Using the method of integration, find the area of the triangle ABC, coordinates of whose vertices area A(1, 2), B (2, 0) and C (4, 3).