Arts (English Medium) Class 12 - CBSE Question Bank Solutions

Area of the region bounded by the curve y² = 4x, y-axis and the line y = 3 is ______.

Find the area under the given curve and given line:

y = x², x = 1, x = 2 and x-axis

Find the area under the given curve and given line:

y = x⁴, x = 1, x = 5 and x-axis

Find the area between the curves y = x and y = x²

Sketch the graph of y = |x + 3| and evaluate `int_(-6)^0 |x + 3|dx`

Find the area enclosed by the parabola 4y = 3x² and the line 2y = 3x + 12

Find the area of the smaller region bounded by the ellipse `x^2/9 + y^2/4` and the line `x/3 + y/2 = 1`

Find the area of the smaller region bounded by the ellipse `x^2/a^2 + y^2/b^2 = 1` and the line `x/a + y/b =   1`

Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B (4, 5) and C (6, 3).

Find the area of the region {(x, y) : y2 ≤ 4x, 4x2 + 4y2 ≤ 9}

Solve the differential equation `cos^2 x dy/dx` + y = tan x

Find `int (cos theta)/((4 + sin^2 theta)(5 - 4 cos^2 theta)) d theta`

Determine the product `[(-4,4,4),(-7,1,3),(5,-3,-1)][(1,-1,1),(1,-2,-2),(2,1,3)]` and use it to solve the system of equations x - y + z = 4, x- 2y- 2z = 9, 2x + y + 3z = 1.

Using the method of integration, find the area of the triangle ABC, coordinates of whose vertices are A (4 , 1), B (6, 6) and C (8, 4).

Find the area enclosed between the parabola 4y = 3x² and the straight line 3x - 2y + 12 = 0.

Find `(dy)/(dx)` at x = 1, y = `pi/4` if `sin^2 y + cos xy = K`

Show that the function f(x) = 4x³ - 18x² + 27x - 7 is always increasing on R.