RD Sharma Class 12 Solutions - Indefinite Integrals - 4

RD Sharma Class 12 Solutions - Indefinite Integrals - 4 | Mathematics (Maths) Class 12 - JEE PDF Download

``` Page 1

28. Question
Write a value of
Let, cos x = t
Differentiating both sides with respect to x
? -dt = sin x dx
Use formula
Again, put t = cos x
29. Question
Write a value of
We know that
1 + sin2x = sin
2
x + cos
2
x + 2sinxcosx
= (sin x + cos x)
2
Let, sin x + cos x = t
Differentiating both sides with respect to x
-dt = (sin x – cos x)dx
Use formula
y = -log t + c
Again, put t = sin x + cos x
Page 2

28. Question
Write a value of
Let, cos x = t
Differentiating both sides with respect to x
? -dt = sin x dx
Use formula
Again, put t = cos x
29. Question
Write a value of
We know that
1 + sin2x = sin
2
x + cos
2
x + 2sinxcosx
= (sin x + cos x)
2
Let, sin x + cos x = t
Differentiating both sides with respect to x
-dt = (sin x – cos x)dx
Use formula
y = -log t + c
Again, put t = sin x + cos x
y = -log(sin x + cos x) + c
30. Question
Write a value of
Let, log x = t
Differentiating both sides with respect to x
Use formula
Again, put t = log x
31. Question
Write a value of
we know ?f(x)g(x)= f(x) ?g(x)-?f' (x) ?g(x)
Let
Given that
Page 3

28. Question
Write a value of
Let, cos x = t
Differentiating both sides with respect to x
? -dt = sin x dx
Use formula
Again, put t = cos x
29. Question
Write a value of
We know that
1 + sin2x = sin
2
x + cos
2
x + 2sinxcosx
= (sin x + cos x)
2
Let, sin x + cos x = t
Differentiating both sides with respect to x
-dt = (sin x – cos x)dx
Use formula
y = -log t + c
Again, put t = sin x + cos x
y = -log(sin x + cos x) + c
30. Question
Write a value of
Let, log x = t
Differentiating both sides with respect to x
Use formula
Again, put t = log x
31. Question
Write a value of
we know ?f(x)g(x)= f(x) ?g(x)-?f' (x) ?g(x)
Let
Given that
32. Question
Write a value of s
we know ?f(x)g(x)= f(x) ?g(x)-?f' (x) ?g(x)
Let
Given that
33. Question
Write a value of
given
34. Question
Write a value of
given
Page 4

28. Question
Write a value of
Let, cos x = t
Differentiating both sides with respect to x
? -dt = sin x dx
Use formula
Again, put t = cos x
29. Question
Write a value of
We know that
1 + sin2x = sin
2
x + cos
2
x + 2sinxcosx
= (sin x + cos x)
2
Let, sin x + cos x = t
Differentiating both sides with respect to x
-dt = (sin x – cos x)dx
Use formula
y = -log t + c
Again, put t = sin x + cos x
y = -log(sin x + cos x) + c
30. Question
Write a value of
Let, log x = t
Differentiating both sides with respect to x
Use formula
Again, put t = log x
31. Question
Write a value of
we know ?f(x)g(x)= f(x) ?g(x)-?f' (x) ?g(x)
Let
Given that
32. Question
Write a value of s
we know ?f(x)g(x)= f(x) ?g(x)-?f' (x) ?g(x)
Let
Given that
33. Question
Write a value of
given
34. Question
Write a value of
given
35. Question
Write a value of
we know that
Given
36. Question
Write a value of
we know that |
Given
37. Question
Write a value of
we know that
Given
Page 5

28. Question
Write a value of
Let, cos x = t
Differentiating both sides with respect to x
? -dt = sin x dx
Use formula
Again, put t = cos x
29. Question
Write a value of
We know that
1 + sin2x = sin
2
x + cos
2
x + 2sinxcosx
= (sin x + cos x)
2
Let, sin x + cos x = t
Differentiating both sides with respect to x
-dt = (sin x – cos x)dx
Use formula
y = -log t + c
Again, put t = sin x + cos x
y = -log(sin x + cos x) + c
30. Question
Write a value of
Let, log x = t
Differentiating both sides with respect to x
Use formula
Again, put t = log x
31. Question
Write a value of
we know ?f(x)g(x)= f(x) ?g(x)-?f' (x) ?g(x)
Let
Given that
32. Question
Write a value of s
we know ?f(x)g(x)= f(x) ?g(x)-?f' (x) ?g(x)
Let
Given that
33. Question
Write a value of
given
34. Question
Write a value of
given
35. Question
Write a value of
we know that
Given
36. Question
Write a value of
we know that |
Given
37. Question
Write a value of
we know that
Given
38. Question
Evaluate:
let
Differentiating on both sides we get,
substituting it in  we get,
39. Question
Evaluate:
let
Differentiating on both sides we get,
Substituting it in  we get,
40. Question
Evaluate:
let
Differentiating on both sides we get,
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Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

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