2012 02 06
Math 124 Midterm #1
I [6] Place the answers in the blanks to the right of the question:
∞
1.
1
∫1 x p converges if
4.
2.
∫
5.
tan(x)dx
π
∫ 4x + 7dx
∫ (sin
2
)
x cos x dx
d
d
6.
tan −1 (x)
sec h(x)
dx
dx
II [6] Show a step or two, even if you think you can do it within your cranium
3.
7.
∫ cos
3
y dy
8.
∫
2xdx
9.
x − 14
2
∫ we
7w
dw
III [24] Do SIX of these, clearly indicating which ones you want marked
10.
∫ (tan x + tan
3
x)dx
y +1
13. ∫ 3
dy
y − y2
11.
14.
∫ (ln x)
∫
2
dx
m2 − 1
dm
m
3
15.
16.
∫ sin
0
2
2
x cos x dx
∫ (sin
−3
π
2
2
∫ t cosh t dt
12.
17.
z
∫e
0
2z
dz
5
)
x − x 2 dx
IV [6] Do TWO of these, clearly indicating which ones you want marked.
For the first two, it is sufficient to say whether the integral converges or not (and why).
∞
0
1
u
1
−4 x
4 2
18. ∫ e dx
19. ∫
dx
20. ∫ u e du
x+4
1
−4
0
V [8] Do TWO of the questions in this section
2
21. Using n = 4 and Simpson's rule, find the approximate definite integral
∫e
x
dx
0
5
22. Likewise using n = 5 and the midpoint rule, evaluate
∫ (x
2
+ 4)dx
0
π
4
3
24. What is the average speed of a particle that traverses the part of the curve y = 3x 2 that is between the yaxis and x = 6 in a total of 2s?
25. The area bounded by y = 2x3, the y-axis and and x = 1 is rotated around the x-axis. Find the surface area
of the resulting solid.
26. Find the centroid of the area between y = x and y = x 3 on the interval 0 ≤ x ≤ 1
2x + 11
27. ∫ 2
dx
x + 7x + 10
23. Find the centroid of y = cos(2x) on the interval 0 ≤ x ≤
VI Bonus (you should not waste time on these unless you are sure you have 75%+ above)
1 + cos x
28. [+2] ∫
dx
29. [+2] Get error bounds for both #21 and #22.
1 − cos x