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

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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 
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