**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.

**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

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

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

**Latest Laptops and Desktops on very small EMI:no extra cost**

**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

**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

You can study

Click the link **here** for rest of the solutions or study the following

** study NCERT solutions Class 12 Maths**

**Exercise 8.3 -Application of Integrals**

**Exercise 8.1-Application of Integrals**

**Exercise 8.2-Application of Integrals**

**Exercise 6.1-Application of Derivatives**

**Exercise 6.2-Application of Derivatives**

**Exercise 6.3 -Application of Derivatives**

**Exercise 6.4- Application of Derivatives**

** Exercise 6.5-Application of Derivations**

**Exercise 5.2 Chapter- Continuity and Differentiability**

**Chapter 5-Continuity and Differentiability**

**Chapter 1- Relations and functions-Download free pdf**

**Class 11 NCERT solutions Chapter 1 of maths, physics and chemistry**

**Chapter 1-Sets(important questions)**

** Chapter 1-Some basic concepts of chemistry**

**Science and Maths NCERT solutions for Class 9 ,10 and 11 classes**

**NCERT Solutions Class 10 Science from chapter 1 to 16**

**You can compensate us by depositing a little money**

**Paytm number 9891436286**

The money collected by us will be used for the education of poor students who leaves their study because of lack of money.

Or you can purchase anything from Amazon from the following link

**Computer acessories**

## Leave a Reply