**NCERT Solutions of class 12 Maths exercise 8.3 -Application of Integrals**

These **NCERT Solutions of class 12 Maths exercise 8.3 of chapter 8-Application of Integrals** are created by an expert CBSE teacher. The** NCERT solutions** written here are the **solutions of class 12 NCERT maths exercise 8.3 of chapter 8-Application of** **Integrals.** We are hundred percent sure that you will like and understand the concept of **maths** used in **exercise 8.3-Application of Integrals** because each **solution** is created by a step by step way,however, if you face any difficulty in understanding the method used here,you can write and suggest us in the comment box.

In this exercise you will study the questions based on the enclosed areas by the curves and the lines.

Q1.Find the area enclosed by the curve whose equations are : y = 2x², x =2 and x-axis

Ans.

The equation of the curve y = 2x², shows that it is passing through the origin and symmetric about y axis.

The required area ABCD

Q2. Find the area enclosed by the curve whose equations are :y = 5x^{4 },x=3.x=7, and x-axis

Ans.

The equation of curve(prabola) y = 5x^{4 }shows that the curve is symmetric about y-axis and it is passing through the origin.

Area of ABCD

**Q3.Find the area enclosed between the curve y²= 3x and line y = 6x.**

Ans. We are given the curve y²= 3x and line y = 6x.

The equation of parabola shows that its vertex is at (0,0) and it is symmetric about the x-axis located at the right side of the y-axis

Solving both equations, we get point of intersections of line and parabola

(6x)² = 3x⇒ 36x² = 3x⇒ 12x = 1⇒ x = 1/12

y = 6 × 1/12 = 1/2

So, as the equation of line shows that it passes through the origin and we have got the point of intersection of the line and the curve is (1/12, 1/2)

Area covered by the curve and the line = Area enclosed by the curve (y²= 3x) OAB – area of the triangle OAB

The area enclosed by the curve (y²= 3x) OAB

Area of ΔOAB

Area covered by the curve and the line

**Q4. Find the area enclosed by the curve y = 2x² and the lines y = 1 and y = 3 and the y-axis.**

Ans. We are given the curve y = 2x² shows that its vertex is at (0,0) and is symmetric about the y-axis and the given lines are y =1 and y = 3

Solving the equation of curve for x

The area enclosed by the curve and the lines y = 1 and y=3 is ar FABDE

It is symmetric about y-axis, so

ar FABDE = 2× ar FABC

ar FABC

ar FABDE

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

** study NCERT solutions Class 12 Maths**

**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**

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**Chapter 5-Continuity and Differentiability**

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Area covered by the curve and the line

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