Definitely Maybe
Indefinitely Probably
The Substitute
Nothing But Net
Area 51
Potpourri
100
Evaluate:
int_3^4(x + 7x^2)dx
What is
539/6
100
Find the integral
int(5x + 7 + 2^x)dx
What is
5/2x^2 + 7x + 2^x/ln2 + C
100
Find the integral
int sin^3x*cosxdx
What is
sin^4x/4 + C
100
If V'(t) is the rate at which water flows into the reservoir at time t (in days). Interpret the meaning of
int_3^9 V'(t)dt
What is the change in the amount of water in the reservoir between days 3 and 9.
100
Estimate the area under the curve
y=x^2
using left endpoints on the interval [1,2] with n = 4. Round to the nearest thousandth.
What is 1.969
100
lim_(x -> 1) (x^2 - 1)/(x^2 + 3x - 4)
What is 2/5
200
Evaluate
int_0^(pi/2)sin(x)dx
What is 1
200
Find the integral
int(3/t - 2/t^2)dt
What is
3 ln|t| + 2/t + C
200
Find the integral
intsqrt(cos(3t))*sin(3t)dt
What is
-2/9*(cos(3t))^(3/2) + C
200
Water is flowing into a tank at a rate of
r(t) = t^2 (ft)^3/min
How much water flows into the tank over the time interval 1 min. to 5 min.?
What is
41.3 ft^3
200
Evaluate
int_0^8f(x)dx
for the following graph of f(x):
What is 9/2
200
lim_(x -> 4) (x - 4)/(sqrt(x) - 2)
What is 4
300
Evaluate
int_4^9(2x+3sqrt(x))dx
What is 103
300
Find the integral
int (x^(3/2) + sqrt(x)/5 - sqrt(x)/x)dx
What is
2/5*x^(5/2) + 2/15*x^(3/2) - 2sqrt(x) + C
300
Find the integral
int(x + 1) / (x^2 + 2x + 19)dx
What is
1/2ln(x^2 + 2x + 19) + C
300
Power P(t) gives the rate of change of energy consumption (in MegaWatts/hour), for a day in September for the city of San Francisco, with t measured in hours starting at midnight. Interpret the meaning of
int_0^24P(t)dt
What is total amount of MegaWatts used in the day.
300
Use geometry to evaluate
int_0^3sqrt(9 - x^2)dx
What is
(9pi)/4
300
A Softball is popped up vertically (from the ground) with an initial velocity of 30 m/s (Assume g = -9.8 m/s^2). Find the time when the object reaches its highest point. What is the height at this point?
What is 45.92 m at t = 3.06 s.
400
Evaluate
int_1^2(e^x+6/x^4)dx
What is
e^2 - e + 7/4
400
Find the integral
int (3cosx - 7sinx)dx
What is
3sinx + 7cosx + C
400
Evaluate
int_1^4 cos(sqrt(x))/sqrt(x)dx
What is
2sin(2) - 2sin(1)
400
The velocity in (m/s) of an object is given by
v(t) = t^2 - 2t
Find the displacement of the object over the time interval [0,5].
What is 50/3 m = 16.7 m
400
Without computing the integral, decide if the
int_-pi^pie^-x*sin(x)dx
is positive or negative.
What is negative
400
Show initial set up for and all approximations using Newton's Method to find the root of
e^x = 2 - 3x
, correct to six decimal places. Use an initial guess of x = 0.
What is 0.242048
500
Evaluate
int_1^2(1 + y^2)/ydy
What is
ln2 + 3/2
500
Find the integral of
int (2xe^x - 8xcosx + x^4)/x dx
What is
2e^x - 8sinx + x^4/4 + C
500
Evaluate
int_0^1x/(1 + 5x^2)dx
What is
ln6/10
500
The velocity in (m/s) of an object is given by
v(t) = t^2 - 2t
Find the distance traveled by the object over the time interval [0,5].
What is 58/3 m = 19.3 m
500
The velocities (in mi/hr) of an automobile moving along a straight highway over a 2-hr period are given by the table below.
Find the midpoint Riemann sum approximation to the displacement on [0,2] with n=4.
What is 117.5 mi
500
lim_(x -> oo) (lnx)^(1/x)
What is 1