Download Calculus I Skills Review Math 150B - Calculus II Write the solution to

Calculus I Skills Review
Math 150B - Calculus II
Write the solution to each derivative from
memory. For any you do not remember,
make a point to memorize them before attempting new material in Calculus II.
1.
d 5
x
dx
3.
5.
7.
d 1
dx x4
2.
4.
d
[cos x]
dx
6.
d
[csc x]
dx
8.
d
[cot x]
9.
dx
11.
13.
d
[ln(x)]
dx
d √
[ x]
dx
d
[sin x]
dx
d
[tan x]
dx
d
[sec x]
dx
d x
10.
[e ]
dx
12.
d
[arcsin x]
dx
d
[arctan x]
dx
Z
26.
Z
28.
Z
sin x dx
27.
sec2 x dx
29.
sec x tan x dx
31.
tan x dx
33.
sec x dx
35.
Z
32.
Z
d 3x 16.
e
dx
d 17.
ln(x5 + 7)
dx
Z
36.
x
Z
38.
p
x2
Z
+ 36 dx
sec2 (πx) dx
x2/3
√
1
x1/3 + 9
37.
Z
39.
d arcsin x2
dx
Write the solution to each integral from
memory.
Z
20.
Z
22.
Z
24.
x5 dx
x
Z
21.
e dx
23.
1
dx
x2
25.
x2
dx
x3 − 27
(sin x)ecos x dx
dx
Z
41.
4
√
Z
x dx
√
3
x dx
Z
1
dx
x
Z
1
√ dx
x
Z
43.
1
e
42.
0
19.
csc x dx
Evaluate each definite integral.
x2
d
15.
dx 3x3 + 8
d 2 cos x
dx
cot x dx
Evaluate each integral using substitution.
40.
d 3
14.
x sin x
dx
18.
csc x cot x dx
Z
Z
34.
csc2 x dx
Z
Z
Evaluate each derivative.
Z
Z
30.
cos x dx
1
16
√
ln(x)
dx
x
1
√
dx
x(1 + x )2
44. Determine the area of the shaded region
shown with y = x(4 − x).
y
4
x
4
Calculus I Skills Review
Math 150B - Calculus II
Answers
1
2. √
2 x
1. 5x4
12. √
16. 3e
5x4
17. 5
x +7
2x
19. √
1 − x4
22. ex + C
√
25. 2 x + C
26. − cos x + C
27. sin x + C
7. − csc x cot x
10. ex
1
1 − x2
14. x2 (3 sin x + x cos x)
3x
4. cos x
9. − csc2 x
8. sec x tan x
1
x
4
x5
28. tan x + C 29. − cot x + C 30. sec x + C
6. sec2 x
5. − sin x
11.
3. −
13.
15.
1
1 + x2
x(16 − 3x3 )
(3x3 + 8)2
31. − csc x + C
33. ln | sin x| + C
36. 31 (x2 + 36)3/2 + C
18. −2 cos x sin x
23. ln |x| + C
√
3
3 x4
21.
+C
4
24. −
1
+C
x
34. ln | sec x + tan x| + C
35. − ln | csc x + cot x| + C
37.
x6
20.
+C
6
32. − ln | cos x| + C
1
3
ln |x3 − 27| + C
16
3
42.
1
π
tan πx + C
√
40. 6 x1/3 + 9 + C
39. −ecos x + C
41.
38.
1
2
43.
3
5
44.
32
3