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**Exercise 8.1 : ** Solutions of Questions on Page Number : **365**

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**Exercise 8.2 : ** Solutions of Questions on Page Number : **371**

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**Exercise Miscellaneous : ** Solutions of Questions on Page Number : **375**

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Next Chapter 9 : Differential Equations >>
**Popular Articles**

Q1 :
**
**

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

**Answer :**

The area of the region bounded by the curve, *y*^{2}
= *x*, the lines,*x* = 1 and *x* = 4, and the
*x*-axis is the area ABCD.

Answer needs Correction? Click Here

Q2 :
**
**

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

**Answer :**

The area of the region bounded by the curve, *y*^{2}
= 9*x*, *x* = 2, and *x* = 4, and the
*x*-axis is the area ABCD.

Answer needs Correction? Click Here

Q3 :
**
**

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

**Answer :**

Q4 :
**
**

Find the area of the region bounded by the ellipse

**Answer :**

Q5 :
**
**

Find the area of the region bounded by the ellipse

**Answer :**

Q6 :
**
**

Find the area of the region in the first quadrant enclosed by
*x*-axis, line and the
circle

**Answer :**

Q7 :
**
**

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

**Answer :**

Q8 :
**
**

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

**Answer :**

Q9 :
**
**

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

**Answer :**

Q10 :
**
**

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

**Answer :**

Q11 :
**
**

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

**Answer :**

Q12 :
**
**

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

**A.** π

**B.**

**C.**

**D. **

**Answer :**

Q13 :
**
**

Area of the region bounded by the curve *y*^{2} =
4*x*, *y*-axis and the line *y* = 3 is

**A.** 2

**B.**

**C.**

**D. **

**Answer :**

Q1 :
**
**

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

**Answer :**

Q2 :
**
**

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

**Answer :**

Q3 :
**
**

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

**Answer :**

Q4 :
**
**

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

**Answer :**

Q5 :
**
**

Smaller area enclosed by the circle *x*^{2} +
*y*^{2} = 4 and the line *x* + *y* = 2 is

**A.** 2 (π - 2)

**B.** π - 2

**C.** 2π - 1

**D.** 2 (π + 2)

**Answer :**

Q6 :
**
**

Area lying between the curve *y*^{2} = 4*x*
and *y* = 2*x* is

**A.**

**B.**

**C.**

**D.**

**Answer :**

Q1 :
**
**

Find the area under the given curves and given lines:

**(i)** *y* = *x*^{2}, *x* = 1,
*x* = 2 and *x*-axis

**(ii)** *y* = *x*^{4}, *x* = 1,
*x* = 5 and *x* -axis

**Answer :**

Q2 :
**
**

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

**Answer :**

Q3 :
**
**

Find the area of the region lying in the first quadrant and
bounded by *y* = 4*x*^{2}, *x* = 0,
*y* = 1 and *y* = 4

**Answer :**

Q4 :
**
**

Sketch the graph of and evaluate

**Answer :**

Q5 :
**
**

Find the area bounded by the curve *y* = sin *x*
between *x* = 0 and *x* = 2π

**Answer :**

Q6 :
**
**

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

**Answer :**

Q7 :
**
**

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

**Answer :**

Q8 :
**
**

Find the area of the smaller region bounded by the ellipse and the line

**Answer :**

Q9 :
**
**

Find the area of the smaller region bounded by the ellipse and the line

**Answer :**

Q10 :
**
**

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

**Answer :**

Q11 :
**
**

Using the method of integration find the area bounded by the curve

[**Hint:** the required region is bounded by lines *x* +
*y* = 1, *x* â€“ *y* = 1,
â€“ *x* + *y* = 1 and
â€“ *x* â€“ *y* = 11]

**Answer :**

Q12 :
**
**

Find the area bounded by curves

**Answer :**

Q13 :
**
**

Using the method of integration find the area of the region bounded by lines:

2*x* + *y* = 4, 3*x* -
2*y* = 6 and *x* - 3*y* + 5 =
0

**Answer :**

Q14 :
**
**

Find the area of the region

**Answer :**

Q15 :
**
**

Area bounded by the curve *y* = *x*^{3}, the
*x*-axis and the ordinates *x* = â€“2
and *x* = 1 is

**A.** â€“ 9

**B.**

**C.**

**D. **

**Answer :**

Q16 :
**
**

The area bounded by the curve, *x*-axis and the
ordinates *x* = â€“1 and *x* = 1 is
given by

**[Hint:** *y* = *x*^{2} if *x* > 0
and *y* = â€“*x*^{2} if
*x* < 0]

**A.** 0

**B.**

**C.**

**D. **

**Answer :**

Q17 :
**
**

The area of the circle *x*^{2} +
*y*^{2} = 16 exterior to the parabola
*y*^{2} = 6*x* is

**A.**

**B.**

**C.**

**D. **

**Answer :**

Q18 :
**
**

The area bounded by the *y*-axis, *y* = cos *x*
and *y* = sin *x* when

**A.**

**B.**

**C.**

**D. **

**Answer :**

Maths Part-2 - Maths : CBSE ** NCERT ** Exercise Solutions for Class 12th for ** Application of Integrals ** ( Exercise 8.1, 8.2, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

- 12th Maths Paper Solutions Set 1 : CBSE Delhi Previous Year 2015
- 12th Maths Paper Solutions Set 2 : CBSE Delhi Previous Year 2015
- 12th Maths Paper Solutions Set 3 : CBSE Delhi Previous Year 2015

- 12th Maths Paper Solutions Set 1 : CBSE Abroad Previous Year 2014
- 12th Maths Paper Solutions Set 1 : CBSE All India Previous Year 2014
- 12th Maths Paper Solutions Set 1 : CBSE Delhi Previous Year 2014

- 12th Maths Paper Solutions Set 1 : CBSE All India Previous Year 2013

- Maths Part-1 : Chapter 5 - Continuity and Differentiability Class 12
- Maths Part-1 : Chapter 6 - Application of Derivatives Class 12
- Maths Part-2 : Chapter 7 - Integrals Class 12
- Maths Part-1 : Chapter 1 - Relations and Functions Class 12
- Maths Part-1 : Chapter 3 - Matrices Class 12
- Maths Part-1 : Chapter 4 - Determinants Class 12
- Maths Part-1 : Chapter 2 - Inverse Trigonometric Functions Class 12
- Maths Part-2 : Chapter 13 - Probability Class 12
- Maths Part-2 : Chapter 9 - Differential Equations Class 12

Exercise 8.1 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Question 10 |

Question 11 |

Question 12 |

Question 13 |

Exercise 8.2 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |