MATH 21 – Midterm 3 Solutions Spring semester 2009
1. F T T F T
2. 6,4xln 4, f, ex, e4, π
3. Z15
0
|v(t)|dt
4. With notation as in the book,
∆x=b−a
n=3−0
3= 1, R3= ∆x(f(1) + f(2) + f(3)) = 1(1 + 4 + 9) = 14
Answer: 14
5. (a) Answer: ln |x|+C
(b) With the substitution u=x3, one gets du
dx = 3x2and
Zx2ex3dx =1
3Zeudu =1
3eu+C=ex3
3+C
Answer: ex3
3+C
(c) Answer: 3 tan−1x+C
6.
Zπ
2
−1
f(x)dx =Z0
−1
f(x)dx +Zπ
2
0
f(x)dx =
Z0
−1
x2+ 1 dx +Zπ
2
0
cos x dx =x3
3+x
0
−1+ sin x
π
2
0=4
3+ 1 = 7
3
Answer: 7
3
1