**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.

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

**Exercise 8.1-Application of Integration**

**Exercise 8.2-Application of Integration**

**Chapter 8-Miscellaneous Exercise Application of Iintegration**

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

Ans.

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

The required area ABCD

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

Ans.

The equation of curve(prabola) yย = 5x^{4ย }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 yยฒ= 3x and line y = 6x.**

Ans. We are given the curve yยฒ= 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)ยฒ = 3xโ 36xยฒ = 3xโ 12x = 1โ x = 1/12

y = 6 ร 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 (yยฒ= 3x) OAB – area of the triangle OAB

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

Area of ฮOAB

Area covered by the curve and the line

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

Ans. We are given the curve y = 2xยฒ 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 = 2ร ar FABC

ar FABC

ar FABDE

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Area covered by the curve and the line