Class 12 RD Sharma Solutions – Chapter 19 Indefinite Integrals – Exercise 19.28
Question 1. Find
Solution:
Let considered x – 1 = t,
so that dx = dt
Thus,
Question 2. Evaluate
Solution:
Let I =
Question 3. Evaluate
Solution:
I =
Hence,
Question 4. Evaluate
Solution:
Let I =
Therefore, I =
Question 5.
Solution:
I =
Let us considered sinx = t
So, on differentiating, we get
cosx dx = dt
I =
Therefore, I =
Question 6. Evaluate
Solution:
I =
Let us considered ex = t
So, on differentiating, we get
exdx = dt
Therefore, I =
Hence, I =
Question 7. Evaluate
Solution:
I =
We already have,
Therefore, I =
Question 8. Evaluate
Solution:
Let us assume I =
Therefore, I =
Question 9. Evaluate
Solution:
Let us assume I =
Therefore, I =
Question 10. Evaluate
Solution:
Let us assume I =
Therefore, I =
Question 11. Evaluate
Solution:
Let us assume I =
Therefore, I =
Question 12. Evaluate
Solution:
Let us assume x2 = t
On differentiating we get
2x dx = dt
Therefore, I =
Hence, I =
Question 13. Evaluate
Solution:
I =
Let us considered x3 = t
So, on differentiating, we get
3x2dx = dt
Therefore, I =
Hence, I =
Question 14. Evaluate
Solution:
I =
Let us considered logx = t
So, on differentiating, we get
1/x dx = dt
Therefore, I =
Hence, I =
Question 15. Evaluate
Solution:
I =
Therefore, I =
Question 16. Evaluate
Solution:
Let I =
I =
Last Updated :
11 Feb, 2021
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