soal latihan persiapan ujian matematika untuk fisika

EXERCISE FOR PREPARING THIRD EXAMINATION
MATHEMATICS I FOR PHYSICS

1. Use the first fundamental theorem of calculus to find
a. f ( x) if



x2

0

f (t ) dt 

c. G '( x) if G ( x)  

x 1

x

b. G '( x) if G ( x)  

1 3
x
3

x2

1

1
dt
t 1
2

f ( z) dz

2. The velocity of an object is

5


t

v(t )  6 
 100
1

if 0  t  100

if 100  t  700
if t  700

a. Assuming that the object is at the origin at time 0, find a formula for its position at time
t (t  0)

b. What is the farthest to the right of the origin that this object ever gets?
c. When, if ever, does the object return to the origin?
3. Oil is leaking at the rate of V '(t )  1 

t

110

form a storage tank that is initially full of 55 gallons.

How much leaks out during the first hour? During the tenth hour? How long until the entire tank
is drained?

4. Water leaks out of a 200-gallon storage tank (initially full) at the rate V '(t )  20  t , where t is
measured in hours and V in gallons. How much water leaked out between 10 and 20 hours? How
long will it take the tank to drain completely?
5. Evaluate each integral
a.
d.
g.
j.





sin x  cos x
dx
tan x

 /4

0

x



2

 .4
/6

x sin 2 x dx

ln x dx

x sec2 x dx

b.

 x cot

2

x dx

e.  sin 3 (2t ) dt
h.
k.



 /2

0



2

1

sin 3t sin t dt

1
dx
1  x4

c.
f.
i.
l.

y



y2

2

 /2

0

x

t

2

 4y  2

e cos x sin x dx

1
dx
 2x  5

t 9

3

dy

 9t

dt