APPLICATION OF INTEGRALS

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$Area={\int }_a^b\left[f\left(x\right)-g\left(x\right)\right]dx+{\int }_c^b\left[g\left(x\right)-f\left(x\right)\right]dx$

Important Questions

Multiple Choice questions-

1. Area lying in the first quadrant and bounded by the circle x² + y² = 4 and the lines x = 0 and x = 2 is

(a) π

(b) $\frac{\pi }{2}$

(c) $\frac{\pi }{3}$

(d) $\frac{\pi }{4}$

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

(a) 2

(b) $\frac{9}{4}$

(c) $\frac{9}{3}$

(d) $\frac{9}{2}$

3. Smaller area enclosed by the circle x² + y² = 4 and the line x + y = 2 is

(a) 2 (π – 2)

(b) π – 2

(c) 2π – 1

(d) 2 (π + 2).

4. Area lying between the curves y² = 4x and y = 2 is:

(a) $\frac{2}{3}$

(b) $\frac{1}{3}$

(c) $\frac{1}{4}$

(d) $\frac{3}{4}$

5. Area bounded by the curve y = x³, the x-axis and the ordinates x = -2 and x = 1 is

(a) -9

(b) – $\frac{15}{4}$

(c) $\frac{15}{4}$

(d) $\frac{17}{4}$

6. The area bounded by the curve y = x|x|, x-axis and the ordinates x = -1 and x = 1 is given by

(a) 0

(b) – $\frac{1}{3}$

(c) $\frac{2}{3}$

(d) $\frac{4}{3}$

7. The area of the circle x² + y² = 16 exterior to the parabola y² = 6x is

(a) $\frac{4}{3}$ (4π – √3)

(b) $\frac{1}{3}$ (4π + √3)

(c) $\frac{2}{3}$ (8π – √3)

(d) $\frac{4}{3}$ (8π + √3)

8. The area enclosed by the circle x² + y² = 2 is equal to

(a) 4π sq. units

(b) 2√2 π sq. units

(c) 4π² sq. units

(d) 2π sq. units.

9. The area enclosed by the ellipse $\frac{x^2}{a^2}$ + $\frac{y^2}{b^2}$ = 1 is equal to

(a) π²ab

(b) πab

(c) πa²b

(d) πab².

10. The area of the region bounded by the curve y = x² and the line y = 16 is

(a) $\frac{32}{3}$

(b) $\frac{256}{3}$

(c) $\frac{64}{3}$

(d) $\frac{128}{3}$

  Very Short Questions:

Long Questions:

Case Study Questions:

1. Ajay cut two circular pieces of cardboard and placed one upon other as shown in figure. One of the circle represents the equation (x – 1)² + y² = 1, while other circle represents the equation x² + y² = 1.

Based on the above information, answer the following questions.

2. Location of three houses of a society is represented by the points A(-1, 0), B(1, 3) and C(3, 2) as shown in figure.

Based on the above information, answer the following questions

Answer Key-

Multiple Choice questions-

Very Short Answer:

Long Answer:

Case Study Answers:

1. Answer :

2. Answer :

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