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

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 Page 1


28. Question
Write a value of 
Answer
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 
Answer
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 
Answer
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 
Answer
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 
Answer
Let, log x = t
Differentiating both sides with respect to x
Use formula 
Again, put t = log x
31. Question
Write a value of 
Answer
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 
Answer
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 
Answer
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 
Answer
Let, log x = t
Differentiating both sides with respect to x
Use formula 
Again, put t = log x
31. Question
Write a value of 
Answer
we know ?f(x)g(x)= f(x) ?g(x)-?f' (x) ?g(x)
Let 
Given that 
32. Question
Write a value of s
Answer
we know ?f(x)g(x)= f(x) ?g(x)-?f' (x) ?g(x)
Let 
Given that 
33. Question
Write a value of 
Answer
given 
34. Question
Write a value of 
Answer
given 
Page 4


28. Question
Write a value of 
Answer
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 
Answer
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 
Answer
Let, log x = t
Differentiating both sides with respect to x
Use formula 
Again, put t = log x
31. Question
Write a value of 
Answer
we know ?f(x)g(x)= f(x) ?g(x)-?f' (x) ?g(x)
Let 
Given that 
32. Question
Write a value of s
Answer
we know ?f(x)g(x)= f(x) ?g(x)-?f' (x) ?g(x)
Let 
Given that 
33. Question
Write a value of 
Answer
given 
34. Question
Write a value of 
Answer
given 
35. Question
Write a value of 
Answer
we know that 
Given 
36. Question
Write a value of 
Answer
we know that |
Given 
37. Question
Write a value of 
Answer
we know that 
Given 
Page 5


28. Question
Write a value of 
Answer
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 
Answer
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 
Answer
Let, log x = t
Differentiating both sides with respect to x
Use formula 
Again, put t = log x
31. Question
Write a value of 
Answer
we know ?f(x)g(x)= f(x) ?g(x)-?f' (x) ?g(x)
Let 
Given that 
32. Question
Write a value of s
Answer
we know ?f(x)g(x)= f(x) ?g(x)-?f' (x) ?g(x)
Let 
Given that 
33. Question
Write a value of 
Answer
given 
34. Question
Write a value of 
Answer
given 
35. Question
Write a value of 
Answer
we know that 
Given 
36. Question
Write a value of 
Answer
we know that |
Given 
37. Question
Write a value of 
Answer
we know that 
Given 
38. Question
Evaluate: 
Answer
let 
Differentiating on both sides we get,
substituting it in  we get,
39. Question
Evaluate: 
Answer
let 
Differentiating on both sides we get,
Substituting it in  we get,
40. Question
Evaluate: 
Answer
let 
Differentiating on both sides we get,
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