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 = 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
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Area covered by the curve and the line