Daily Practice Problems

Class 12 Maths

Application of Integrals

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 4x^{2} + 4y^{2} = 9 which is interior to the parabola x^{2} = 4y.

**Question 3:**

Find the area bounded by curves (x – 1)^{2} + y^{2} = 1 and x^{2} + y^{2} = 1.

**Question 4:**

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

**Question 5:**

Find the smaller area enclosed by the circle x^{2} + y^{2} = 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 x^{2} = 4y and the line x = 4y – 2.

**Question 8:**

Find the area bounded by the curves y^{2} = 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 – x^{2}) 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 = x^{3} 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 = x^{3}, 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 y^{2} = 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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