Daily Practice Problems
Class 12 Maths
Application of Integrals Question 1:

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

Question 2:

Find the area of the circle 4x2 + 4y2 = 9 which is interior to the parabola x2 = 4y.

Question 3:

Find the area bounded by curves (x – 1)2 + y2 = 1 and x2 + y2 = 1.

Question 4:

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

Question 5:

Find the smaller area enclosed by the circle x2 + y2 = 4 and the line x + y = 2.

Question 6:

Find the area bounded by the curve y = x|x|, x-axis and the ordinates x = –1 and x = 1.

Question 7:

Find the area bounded by the curve x2 = 4y and the line x = 4y – 2.

Question 8:

Find the area bounded by the curves y2 = 4x and y = x.

Question 9:

Area bounded by the curve y = sin x and the x-axis between x = 0 and x = 2π is ______.

Question 10:

Area of the region bounded by the curve y = √(49 – x2) and the x-axis is _____.

Question 11:

Area of the region bounded by the curve x = 2y + 3, the y-axis and between y = -1 and y = 1 is _____.

Question 12:

The area enclosed between the graph of y = x3 and the lines x = 0, y = 1, y = 8 is _____.

Question 13:

Find the area of the region bounded by the curve y² = x, the y-axis and between y = 2 and y = 4.

Question 14:

The area bounded by the curve y = x3, the x-axis and two ordinates x = 1 and x = 2 is _____.

Question 15:

Find the area of the region bounded by the curve y = 1/x, x-axis and between x = 1, x = 4.

Question 16:

The area of the region bounded by the curve y² = x, the y-axis and between y = 2 and y = 4 is 56/3 sq units. State whether it is true or false?

Question 17:

Find the area of the region bounded by the circle x² + y² = 1.

Question 18:

What is the area of the parabola y2 = x bounded by its latus rectum?

Question 19:

Find the area of the region bounded by the curve y = e-2x and x-axis for x (-1, 1).

Question 20:

Using integration find the area of the triangular region whose sides have the equations y = 2x + 1, y = 3x + 1 and x = 4.

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