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

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).

Using integration, find the area of the region {(x, y) : x² + y² ≤ 1 ≤ x + y}.

Find the coordinates of a point of the parabola y = x² + 7x + 2 which is closest to the straight line y = 3x − 3.

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

Find the area of the smaller region bounded by the ellipse \[\frac{x^2}{9} + \frac{y^2}{4} = 1\] and the line \[\frac{x}{3} + \frac{y}{2} = 1 .\]

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)`.

Using integration, find the area of the region in the first quadrant enclosed by the line x + y = 2, the parabola y² = x and the x-axis.

Using integration, find the area of the region `{(x, y): 0 ≤ y ≤ sqrt(3)x, x^2 + y^2 ≤ 4}`

Make a rough sketch of the region {(x, y): 0 ≤ y ≤ x², 0 ≤ y ≤ x, 0 ≤ x ≤ 2} and find the area of the region using integration.

Using integration, find the area of the region bounded by the curves x² + y² = 4, x = `sqrt(3)`y and x-axis lying in the first quadrant.

Find the area of the region enclosed by the curves y² = x, x = `1/4`, y = 0 and x = 1, using integration.

Using Integration, find the area of triangle whose vertices are (– 1, 1), (0, 5) and (3, 2).

Find the area of the smaller region bounded by the curves `x^2/25 + y^2/16` = 1 and `x/5 + y/4` = 1, using integration.

Find the area of the minor segment of the circle x² + y² = 4 cut off by the line x = 1, using integration.