Chapters
- Exercise 1
- Exercise 2
- Exercise 3
- Exercise 4
- Exercise 5
- Exercise 6
- Exercise 7
- Exercise 8
- Exercise 9
- Exercise 10
- Exercise 11
- Solution of exercise 1
- Solution of exercise 2
- Solution of exercise 3
- Solution of exercise 4
- Solution of exercise 5
- Solution of exercise 6
- Solution of exercise 7
- Solution of exercise 8
- Solution of exercise 9
- Solution of exercise 10
- Solution of exercise 11
Calculate the following integrals:
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Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Exercise 9
Exercise 10
Exercise 11
Solution of exercise 1
Solution of exercise 2
Solution of exercise 3
If , then .
If , then
Suppose , then
If , then
If u = 6x + 10, then u' = 6
If v' = , then
Solution of exercise 4
If u = lnx, then
If v' = 1, then v = x
Solution of exercise 5
If , then
If v' = cos x, then v = sin x
If , then
If v' = sin x, then v = -cos x
Solution of exercise 6
To calculate A, B and C, we substitute x with −3:
Derive and replace with −3:
x = -3 -20 = B
Derive again:
6 = 2A A = 3
Also, the coefficients can be found by realizing the operations and equaling coefficients:
-2 = 19 + B
5 = 27 + C
3 = A
B = -20
C = 38
Solution of exercise 7
Solution of exercise 8
t = -1 1 = -2A A =
t = 1 1 = 2B B =
Solution of exercise 9
Solution of exercise 10
=
Solution of exercise 11