JEE Exam  >  JEE Notes  >  Mathematics (Maths) Class 12  >  RD Sharma Class 12 Solutions - Definite Integrals - 2

RD Sharma Class 12 Solutions - Definite Integrals - 2 | Mathematics (Maths) Class 12 - JEE PDF Download

Download, print and study this document offline
Please wait while the PDF view is loading
 Page 1


6. Question
Evaluate of each of the following integral:
Answer
Let us assume 
By integration property, we know,
Thus
We know
We know  and a being the upper and lower limits respectively
I = [a – 0]
I = a.
7. Question
Evaluate of each of the following integral:
Answer
Let us assume,
By integration property,
Page 2


6. Question
Evaluate of each of the following integral:
Answer
Let us assume 
By integration property, we know,
Thus
We know
We know  and a being the upper and lower limits respectively
I = [a – 0]
I = a.
7. Question
Evaluate of each of the following integral:
Answer
Let us assume,
By integration property,
Thus
We know
we know since  b and a being the upper and lower limits
8. Question
Evaluate of each of the following integral:
.
Answer
Let us assume  .......equation 1
By property, we know that 
Thus
 .....equation 2
Page 3


6. Question
Evaluate of each of the following integral:
Answer
Let us assume 
By integration property, we know,
Thus
We know
We know  and a being the upper and lower limits respectively
I = [a – 0]
I = a.
7. Question
Evaluate of each of the following integral:
Answer
Let us assume,
By integration property,
Thus
We know
we know since  b and a being the upper and lower limits
8. Question
Evaluate of each of the following integral:
.
Answer
Let us assume  .......equation 1
By property, we know that 
Thus
 .....equation 2
Adding the equations 1 and 2, we get,
We know
Trigonometric formula
We know
Thus
We know
Thus
we know b and a being the upper and lower limit
Since sinp = 0 and sin (– ?) = – sin?
Thus
Page 4


6. Question
Evaluate of each of the following integral:
Answer
Let us assume 
By integration property, we know,
Thus
We know
We know  and a being the upper and lower limits respectively
I = [a – 0]
I = a.
7. Question
Evaluate of each of the following integral:
Answer
Let us assume,
By integration property,
Thus
We know
we know since  b and a being the upper and lower limits
8. Question
Evaluate of each of the following integral:
.
Answer
Let us assume  .......equation 1
By property, we know that 
Thus
 .....equation 2
Adding the equations 1 and 2, we get,
We know
Trigonometric formula
We know
Thus
We know
Thus
we know b and a being the upper and lower limit
Since sinp = 0 and sin (– ?) = – sin?
Thus
9. Question
Evaluate of each of the following integral:
Answer
Let us assume 
By property, we know,
We know
We know b and a being the upper and lower limits
Since 
I = 2.
10. Question
Evaluate of each of the following integral:
, n ? N, n = 2
Answer
Let us assume  ..... equation 1
By property, we know that,
Page 5


6. Question
Evaluate of each of the following integral:
Answer
Let us assume 
By integration property, we know,
Thus
We know
We know  and a being the upper and lower limits respectively
I = [a – 0]
I = a.
7. Question
Evaluate of each of the following integral:
Answer
Let us assume,
By integration property,
Thus
We know
we know since  b and a being the upper and lower limits
8. Question
Evaluate of each of the following integral:
.
Answer
Let us assume  .......equation 1
By property, we know that 
Thus
 .....equation 2
Adding the equations 1 and 2, we get,
We know
Trigonometric formula
We know
Thus
We know
Thus
we know b and a being the upper and lower limit
Since sinp = 0 and sin (– ?) = – sin?
Thus
9. Question
Evaluate of each of the following integral:
Answer
Let us assume 
By property, we know,
We know
We know b and a being the upper and lower limits
Since 
I = 2.
10. Question
Evaluate of each of the following integral:
, n ? N, n = 2
Answer
Let us assume  ..... equation 1
By property, we know that,
 ...... equation 2
Adding equation 1 and equation 2
 + 
We know
We know  b and a being the upper and lower limit
11. Question
Evaluate of each of the following integral:
Answer
Let us assume 
We know 
Thus
We know
Thus
Since 
Read More
204 videos|290 docs|139 tests

Top Courses for JEE

204 videos|290 docs|139 tests
Download as PDF
Explore Courses for JEE exam

Top Courses for JEE

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

video lectures

,

RD Sharma Class 12 Solutions - Definite Integrals - 2 | Mathematics (Maths) Class 12 - JEE

,

pdf

,

Extra Questions

,

Sample Paper

,

past year papers

,

RD Sharma Class 12 Solutions - Definite Integrals - 2 | Mathematics (Maths) Class 12 - JEE

,

Previous Year Questions with Solutions

,

ppt

,

shortcuts and tricks

,

Summary

,

Viva Questions

,

Important questions

,

MCQs

,

Objective type Questions

,

Semester Notes

,

RD Sharma Class 12 Solutions - Definite Integrals - 2 | Mathematics (Maths) Class 12 - JEE

,

study material

,

Free

,

mock tests for examination

,

Exam

,

practice quizzes

;