Wednesday, January 14
Clicker Questions
Clicker Question 1
A definite integral
Z
e2
1
dt.
t
Z
e2
Evaluate
1
A. 2, since
1
1
dt = ln x
t
1
B. 1 − 4
e
1
C. 2 − 1
e
D. ln(e2 ) − 1
E. none of the above
e2
1
= ln(e2 ) − ln(1) = 2 − 0
Clicker Question 2
Recalling properties of derivatives
Suppose that f (x) and g(x) are differentiable functions, and
f 0 (x) = g0 (x) for all x. What is the relationship between f and g?
A. f (x) is g(x) times a constant
B. f (x) is g(x) plus a constant
C. f (x) and g(x) add to 0
D. f (x) and g(x) are the same
function
E. no relationship, totally random
Clicker Question 3
An indefinite integral
Z
If a > 0 is a constant, what is
A.
ax dx?
ax+1
+C
x+1
B. ax + C
ax+1
+C
a+1
1 x
d
1 x
1 d(ax )
1
D.
a + C, as
a +C =
=
(ln a)ax
ln a
dx ln a
ln a dx
ln a
C.
E. (ln a)ax + C
Clicker Question 4
What’s the right question?
√
Which of the following indefinite integrals equals x 2x + 3 + C ?
Z
A.
Z
B.
Z
√
2x + 3 dx
√ 3 x + 3 dx
√
x
dx
2x + 3
Z
3x + 3
√
D.
dx
2x + 3
E. none of the above
C.
√
Indefinite integrals: sometimes
easier to check than find!
d √
x 2x + 3 + C
dx
√
1
2
= 1 · 2x + 3 + x · √
+0
2 2x + 3
1
2
2x + 3
+x· √
=√
2
2x + 3
2x + 3
3x + 3
=√
2x + 3