1 Integration Z - McGill University

[Pages:2]1 Integration

Evaluate the integral.

1. 4(1 + x)2dx

1

2

2.

x2 - x dx

0

(x-1 + x)2

3.

x2 dx

2

4. x2dx

0

x3 - 3x + 5

5.

dx

3x

0

6. (x2 - 4)2dx

-2

7.

10x4

-

1 x3

+

15 x3

-

7

dx

8.

2 1

2x3

+

5 x4

dx

9.

(2x

+

1)(x

-

1)

dx

x

3x5 + 6

10.

2x3 dx

1

11. (2t + 3t2)dt

0

9

12. x + x dx

1

13.

8 1

6x2

-

3x

+

2 x3

dx

14.

2x

-

1 x2

+

ex

dx

13

12

1

15.

+

-

dx

x

x

x

16. 3x2 -2x + 5 dx 4x

17. (2x3 - 1)(x2 + 5)dx

(3x - 2)2

18.

dx

4x

3 21

19.

3x

-

x3

+

3x

dx

2

20. (2x2 + x - 1)dx

1

2y4 + 1

21.

3y3 dy

22.

x+1

-

1 x

+

1 x2

+ sin x

- ex

dx

4

23. x + 2 x + 1 + dx

x

24. tan2 xdx

sin x 25. cos2 x dx

/4

26.

sec2 xdx

0

27. sin xdx

0

28. cos xdx

0

1

29.

dx

1 + sin x

cot x

30.

dx

sin x

31.

dx

sec x

3 32. 1 - cos2 x dx

-1 33. cos2 x dx

1

Answers:

1.

119 6

2.

2 3

12 3. - 3x3 - x + x + C

4.

8 3

5. 3 x11/3 - 9 x5/3 + 15 x2/3 + C

11

5

2

6.

256 15

7.

2x5 +

1 2x2

+ 6x5/2 - 7x + C

8.

215 24

4x5/2 2x3/2

9.

-

-2 x+C

5

3

x3 3 10. 2 - 2x2 + C

11. 2

12.

172 3

13.

64751 64

14. 4x3/2 + 1 + ex + C 3x

11 15. - 2x2 - x - ln |x| + C

12x11/4 8x7/4 20x3/4

16.

-

+

+C

11

7

3

x6 5x4 x3 17. + - - 5x + C

323

9x2 18. - 3x + ln |x| + C

8

9x2/3 1 ln |x| 19. 2 + x2 + 3 + C

20.

31 6

21.

1 3

y2

-

1 6y2

+C

22. 2 x3/2 + x - ln |x| - 1 - cos x - ex + C

3

x

23.

x2

+

4 x3/2

+

x+8 x

+C

23

24. tan x - x + C

25. sec x + C

26. 1 27. 2 28. 0 29. tan x - sec x + C [Hint: Multiply numerator

and denominator by 1 - sin x.] 30. - csc x + C 31. sin x + C 32. -3 cot x + C 33. - tan x + C

2

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download