84 Part I: The Questions
613. A new bird population that is introduced
into a refuge starts with 100 birds and
increases at a rate of p'(t) birds per month.
What does 100 0
6
+
′
∫ p t dt
( ) represent?
614. If v(t) is the velocity of a particle in meters
per second, what does v t dt
( )
0
10
∫
represent?
615. If a(t) is the acceleration of a car in meters
per second squared, what does a t dt
( )
3
5
∫
represent?
616. If P '(t) represents the rate of production of
solar panels, where t is measured in weeks,
what does
′
∫ P t dt
( )
2
4
represent?
617. The current in a wire I(t) is defined as the
derivative of the charge, Q'(t) = I(t). What
does I t dt
t
t
( )
1
2
∫
represent if t is measured
in hours?
618. I '(t) represents the rate of change in your
income in dollars from a new job, where t is
measured in years. What does
′
∫ I t dt
( )
0
10
represent?
606. x
x
x
dx
3
25
5
−
+
∫
607. tan
sin
2
2
x
x
dx
∫
608.
cos
cos
sin
2x
x
x
dx
+
∫
609. cos
sin
2
2
x
x
dx
∫
610. cos cos tan
sec
x
x
x
x
dx
+
2
2
∫
Understanding the Net
Change Theorem
611–619 Use the net change theorem to interpret the
given definite integral.
611. If w'(t) is the rate of a baby’s growth in
pounds per week, what does
′
∫ w t dt
( )
0
2
represent?
612. If r(t) represents the rate at which oil leaks
from a tanker in gallons per minute, what
does
r t dt
( )
0
180
∫
represent?