**CBSE Class 12 Maths Chapter-8 Important Questions – Free PDF Download**

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**CBSE Class 12 Mathematics Important Questions Chapter 8 – Application of Integrals**

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**4 Mark Questions**

**1. Find the area of the region bounded by the curve y ^{2} = x and the lines x = 1, x = 4 and x – axis.**

**Ans.**y

^{2}= x is the equation of parabola and x = 1, x = 4 and x – axis

Req. area =

**2. Find the area of the region bounded by y ^{2} = 9x, x =2, x = 4 and the x – axis in the first quadrant.**

**Ans.**y

^{2}= 9x, x = 2, x = 4, x – axis in the first quadrant.

**3. Find the area of the region bounded by the parabola y = x ^{2} + 1 and the lines y = x,**

**x = 0 and x = 2.**

**Ans.**y = x

^{2}+ 1

y = x, x = 0, x = 2

**4. Find area of the region bounded x ^{2} = 4y, y = 2, y = 4 and the y – axis in the first quadrant.**

**Ans.**x

^{2}= 4y, y = 2, y = 4 y – axis in the first quadrant

**5. Find the area of the region bounded by the ellipse.**

**Ans.**

**6. Find the area of the region in the first quadrant enclosed by x – axis and by the circle x ^{2} + y^{2 }= 4.**

**Ans.**

x – axis

in first quadrant.

**7. Draw the graph of the curve and find the area bounded by this curve and the coordinate axis.**

**Ans.**

**8. The area between x = y ^{2} and x = 4 is divided into equal parts by the line x = a, find the value of a.**

**Ans.**x = y2

x = 4

x = a

ATQ

**9. Find the area of the region bounded by the parabola y = x ^{2} and y = |x|.**

**Ans.**y = x

^{2}

**10. Find the area of ellipse **

**Ans.**

**11. Find the area bounded by the curve x ^{2} = 4y and the line x = 4y – 2.**

**Ans.**x

^{2}= 4y

x = 4y – 2

Req. area =

**12. Find the area of the region bounded by the curve y ^{2} = 4x and the line x = 3.**

**Ans.**y

^{2}= 4x

x = 3

**13. Find the area between the curve y = |x + 3|, the x – axis and the lines x = -6 and x = 0.**

**Ans.**

**14. Find the Area lying in the first quadrant and bounded by the circle x ^{2} + y^{2} = 4 and the lines x = 0 and x = 2.**

**Ans.**

Area

**15. Find the Area of the region bounded by the curve y ^{2} = 4x, y – axis and the line y = 3.**

**Ans.**

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

**Ans.**

On solving (1) and (2)

**17. Find the area of the region bounded by the parabolas y ^{2} = 4ax and x^{2} = 4ay, a > 0.**

**Ans.**

**18. Find the area of the region bounded by the curves y = x ^{2} + 2, y = x, x = 0 and x = 3.**

**Ans.**

**19. Find the area of the region **

**Ans.**

**20. Find the area bounded by the curves **

**Ans. **

**21. Find the area of the region:**

**Ans.**

**22. Using integration find the area of the triangular region whose side have the equations y = 2x**

**+ 1, y = 3x + 1, and x = 4.**

**Ans.**

On solving

**23. Calculate the area of the region enclosed between eh circles:**

**x ^{2} + y^{2} = 16 and (x + 4)^{2} + y^{2} =16.**

**Ans.**

Intersecting at x = -2

**24. Find the area of the circle x ^{2} = y^{2} = 15 exterior to the parabola y^{2} = 6x **

**Ans.**

**25. Find the area bounded by the y – axis, y = cosx and y = sinx, **

**Ans.**

**26. Using integration, find the area of the region in the first quadrant enclosed by the**

**x – axis, the line y = x and the circle x ^{2} + y^{2} = 32.**

**Ans.**

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**6 Marks Questions**

**1. Find the area of the region bounded by the ellipse.**

**Ans.**

Required area

**2. Find the area of the smaller part of the circle x ^{2} + y^{2} = a^{2} cut off by the line **

**Ans.**

**3. Prove the area of a circle of radius r is square units.**

**Ans.**

**4. Find the area enclosed between the curve y = x ^{3} and the line y = x.**

**Ans.**

**5. Find the area of the circle 4x ^{2} + 4y^{2} = 9 which is interior to the parabola y^{2} = 4x.**

**Ans.**

**6. Using integration, find the area of region bounded by the triangle whose vertices are**

**(-1, 0),(1, 3) and (3, 2).**

**Ans.**

A (-1, 0) B (1, 3) C (3, 2)

Equation of AB

Similarly

Equation of BC

Equation of AC

**7. Draw a rough sketch of the region and find the area enclosed by the region using method of integration.**

**Ans.**

On solving

**8. Using integration, find the area of the region given below: .**

**Ans.**

**9. Compute the area bounded by the lines x + 2y = 2, y – x = 1 and 2x + y = 7.**

**Ans.**

**10. Find Smaller area enclosed by the circle x ^{2} + y^{2} = 4 and the lines x + y = 2.**

**Ans.**

Finding smaller area. On solving (1) and (2)

**11. Find the area between the curves y = x and y = x ^{2}.**

**Ans.**

On solving x = 0, 1

**12. Sketch the graph of y = |x + 3| and evaluate **

**Ans.**

**13. Find the area bounded by the curve y = sinx between x = 0 and x = 2**

**Ans.**

**14. Find the area enclosed by the parabola y ^{2} = 4ax and the line y = mx.**

**Ans.**

**15. Find the area of the region **

**Ans.**

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

**Ans.**

**17. Find the area of the smaller region bounded by the ellipse and the line **

**Ans.**

is the equation of ellipse and

is the equation of intercept form

**18. Find the area of the smaller region bounded by the ellipse and the line **

**Ans. **

**19. Find the area of the region enclosed by the parabola x ^{2} = y, the line y = x +2 and the x– axis.**

**Ans.**

**20. Using method of integration, find the area bounded by the curve |x| + |y| = 1.**

**Ans.**

**21. Find area bounded by curves **

**Ans. **

**22. Using 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).**

**Ans.**

**23. Using method of integration, find the area of the region bounded by lines:**

**2x + y = 4, 3x – 2y = 6**

**and x – 3y + 5 = 0.**

**Ans.**

**24. Find the area of two regions **

**Ans.**