**NCERT Solutions of class 12 maths Miscellaneous exercise -Application of Integrals**

The NCERT solutions of miscellaneous exercise of chapter 8-Application of Integrals are a summary of all the methods used in all the exercises of chapter 8-Application of Integrals, therefore in this respect, NCERT solutions of miscellaneous exercise are very important for students.All the questions of miscellaneous exercise are solved by the expert by a step by step method so each student will understand the solution clearly.

**Exercise 8.1-Application of Integration**

**Exercise 8.2-Application of Integration**

**Exercise 8.3-Application of Integration**

**NCERT Solutions of Maths for Class 12**

**NCERT solutions of class 12 maths**

Chapter 1-Relations and Functions | Chapter 9-Differential Equations |

Chapter 2-Inverse Trigonometric Functions | Chapter 10-Vector Algebra |

Chapter 3-Matrices | Chapter 11 – Three Dimensional Geometry |

Chapter 4-Determinants | Chapter 12-Linear Programming |

Chapter 5- Continuity and Differentiability | Chapter 13-Probability |

Chapter 6- Application of Derivation | CBSE Class 12- Question paper of maths 2021 with solutions |

Chapter 7- Integrals | |

Chapter 8-Application of Integrals |

**Q1. Find the area under the given curve and given lines**

**(i) y = x² , x = 1, x =2 and x-axis**

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

Ans.

(i) We are given the curve y = x² and the lines x = 1, x =2

Area covered by the curve,x-axis and the given lines = arABCD

(ii) We are given the curve y = x^{4}, x=1, x= 5 and the lines x = 1, x =2

Area covered by the curve, x-axis and the given lines = arABCD

**Q2. Find the area between the curves y = x and y = x²**

Ans. We are given the equations of curve y = x² and y = x

Putting y = x, in y = x²

x = x² ⇒ x= 0 and x =1,again putting x = 0 and x= 1 in one of the equations, we get y=0 and y=1

Therefore both of curve and the line intersect each other at origin (0,0) and (1,1)

Area covered by the line and the curve , area OCB = ar ΔOAB – ar OABCO

ar OABCO = 1/3 sq.unit

OA = 1 unit and AB = 1 unit

**Q3. Find the area of the region lying in the first quadrant and bounded by y = 4x², x = 0, y =1 and y = 4.**

Ans. The given curve is y = 4x² and the lines are x = 0, y =1 and y = 4.

The area covered by the curve y = 4x² and the lines are x = 0(y-axis), y =1, and y = 4 is ar ABCD

From the equation of curve, y = 4x², we have

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**Q4. Sketch the graph of and evaluate **

rom the equation of curve, y = 4x², we have

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**Q4. Sketch the graph of and evaluate **

Ans.Solutions of the given equation

x | -6 | -5 | -4 | -3 | -2 | -1 | 0 |

y | 3 | 2 | 1 | 0 | 1 | 2 | 3 |

The graph of the given equation is drawn as follows

**= – 9 + 18 = 9**

**Q5. Find the area bounded by the curve y = sinx between x = 0 and x = 2π.**

Ans.The graph of the curve y = sinx between x = 0 and x = 2π, is shown below

The area bounded by the curve y = sinx, x = 0 and x = 2π

=Area of OAB + area of BCD

= 2 + 2 = 4 sq.unit

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**NCERT Solutions of class 9 maths**

Chapter 1- Number System | Chapter 9-Areas of parallelogram and triangles |

Chapter 2-Polynomial | Chapter 10-Circles |

Chapter 3- Coordinate Geometry | Chapter 11-Construction |

Chapter 4- Linear equations in two variables | Chapter 12-Heron’s Formula |

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Chapter 6-Lines and Angles | Chapter 14-Statistics |

Chapter 7-Triangles | Chapter 15-Probability |

Chapter 8- Quadrilateral |

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**NCERT solutions of class 11 maths**

Chapter 1-Sets | Chapter 9-Sequences and Series |

Chapter 2- Relations and functions | Chapter 10- Straight Lines |

Chapter 3- Trigonometry | Chapter 11-Conic Sections |

Chapter 4-Principle of mathematical induction | Chapter 12-Introduction to three Dimensional Geometry |

Chapter 5-Complex numbers | Chapter 13- Limits and Derivatives |

Chapter 6- Linear Inequalities | Chapter 14-Mathematical Reasoning |

Chapter 7- Permutations and Combinations | Chapter 15- Statistics |

Chapter 8- Binomial Theorem | Chapter 16- Probability |

**CBSE Class 11-Question paper of maths 2015**

**CBSE Class 11 – Second unit test of maths 2021 with solutions**

**NCERT solutions of class 12 maths**

Chapter 1-Relations and Functions | Chapter 9-Differential Equations |

Chapter 2-Inverse Trigonometric Functions | Chapter 10-Vector Algebra |

Chapter 3-Matrices | Chapter 11 – Three Dimensional Geometry |

Chapter 4-Determinants | Chapter 12-Linear Programming |

Chapter 5- Continuity and Differentiability | Chapter 13-Probability |

Chapter 6- Application of Derivation | CBSE Class 12- Question paper of maths 2021 with solutions |

Chapter 7- Integrals | |

Chapter 8-Application of Integrals |

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