# NCERT SOLUTIONS FOR CLASS 12 Maths Chapter 8 Application of Integral

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NCERT SOLUTIONS FOR CLASS 12 Maths Chapter 8 Application of Integral is all about the applications of whatever you read in the previous chapter Integrals. Limits of integration, Properties of definite integrals.application of indefinite integrals, area of the region bounded by the curve, area of the region enclosed between two curves, Leibnitz Rule, properties of definite integral, properties of the integral function, gamma function, properties of the gamma function, Walli’s formula, integration by the first principle.

New terminologies that can be found in this chapters are Area Under Simple Curve,The area of region bounded by a curve and a line,Area Between Two Curves. Although there are not so more new terminologies its a difficult chapter to get mugged up in short period.Hence,For the easiness regarding this topic STUDY HUNT Provides you the simpler PDF File for NCERT SOLUTIONS FOR CLASS 12 Maths Chapter 8 Application of Integral.

You will be learning how to find the are of an enclosed curve using Leibnitz Rule,using substitution method to evaluate the definite integrals.You will also know the properties of Definite Integral and Integral function along with gamma function properties of gamma functions and walli’s formula.Besides of that finding an area of a circle bounded in a line and circle and parabola and ellipse as well.You will be able to find the area enclosed by two curves, area of curves given by polar equations, area of parametric curves.

# EXAMPLE SOLUTIONS FOR NCERT SOLUTIONS FOR CLASS 12 MATHS CHAPTER 8 APPLICATION OF INTEGRALS.

1. Find the area of the region bounded by the curve  and the lines  and the  axis.

Ans. Equation of the curve (rightward parabola) is

……….(i)

[From eq. (i)]

=  =

=   =  sq. units

### 2. Find the area of the region bounded by  and the axis in the first quadrant.

Ans. Equation of the curve (rightward parabola) is

……….(i)

Required area (shaded region) bounded by curve  (vertical lines ) and axis in first quadrant.

[From eq. (i)]

=

=

=   =  sq. units

### 3. Find the area of the region bounded by  and the  axis in the first quadrant.

Ans. Equation of curve (parabola) is    ……….(i)

Required (shaded) area bounded by curve  (Horizontal lines ) and axis in first quadrant.

=  =  sq. units

### 4. Find the area of the region bounded by the ellipse

Ans. Equation of ellipse is  ……….(i)

Here

From eq. (i),

……….(ii)

for arc of ellipse in first quadrant.

Ellipse (i) ia symmetrical about axis,

( On changing  in eq. (i), it remains unchanged)

Ellipse (i) ia symmetrical about axis,

( On changing  in eq. (i), it remains unchanged)

Intersections of ellipse (i) with axis

Putting  in eq. (i),

Therefore, Intersections of ellipse (i) with axis are (0, 4) and .

Intersections of ellipse (i) with axis

Putting  in eq. (i),

Therefore, Intersections of ellipse (i) with axis are (0, 3) and .

Now Area of region bounded by ellipse (i) = Total shaded area

= 4 x Area OAB of ellipse in first quadrant

[ At end B of arc AB of ellipse;  and at end A of arc AB ; ]

=

=

sq. units

### 5. Find the area of the region bounded by the ellipse

Ans. Equation of ellipse is

Here

From eq. (i),

……….(ii)

for arc of ellipse in first quadrant.

Ellipse (i) ia symmetrical about axis,

( On changing  in eq. (i), it remains unchanged)

Ellipse (i) ia symmetrical about axis,

( On changing  in eq. (i), it remains unchanged)

Intersections of ellipse (i) with axis

Putting  in eq. (i),

Therefore, Intersections of ellipse (i) with axis are (0, 2) and .

Intersections of ellipse (i) with axis

Putting  in eq. (i),

Therefore, Intersections of ellipse (i) with axis are (0, 3) and .

Now Area of region bounded by ellipse (i) = Total shaded area

= 4 x Area OAB of ellipse in first quadrant

[ At end B of arc AB of ellipse;  and at end A of arc AB ; ]

=

sq. units

### #CLEARING OUT THE APPLICATIONS OF INTEGRALS.

After knowing about the applications of integrals briefly we provided you the NCERT Solutions. We strongly suggest and encourage the students to go through all the solutions from the PDF File.As they are the most probable questions along with answers. It has reduces time of the students.Understandable PDF File will help them to secure better marks in the NCERT Board Examination.

### #MOTIVATION FOR THE STUDENTS.

We the team of STUDYHUNT kindly request all the students to schedule the time table for the study. It means it will allow you to remain in discipline as well as you can play and enjoy the rest of your time except the scheduled one. By this you will get limited and there will be no chance of wastage of time.This interns, You all will score better marks in your Examinations.