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

RD Sharma Class 12 Solutions - Definite Integrals - 2

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
Explore Courses for JEE exam
Related Searches
Viva Questions, ppt, Summary, Free, study material, Important questions, practice quizzes, pdf , RD Sharma Class 12 Solutions - Definite Integrals - 2, Extra Questions, video lectures, Exam, RD Sharma Class 12 Solutions - Definite Integrals - 2, Sample Paper, shortcuts and tricks, mock tests for examination, Objective type Questions, past year papers, Previous Year Questions with Solutions, MCQs, RD Sharma Class 12 Solutions - Definite Integrals - 2, Semester Notes;