Definitely Maybe
Indefinitely Probably
The Substitute
Nothing But Net
Area 51
100
Evaluate:
int_3^4(x + 7x^2)dx
What is 539/6
100
Find the integral
int(3x^3+5x-7)dx
What is
3/4 x^4+5/2 x^2-7x+C
100
Find the integral
int 3x^2(x^3+2)^5dx
What is
1/6 (x^3+2)^6 + 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(V'(t),t,3,9).
What is the amount of water that flows into the reservoir between days 3 and 9.
100
Find the area under the curve y=x^2 from x = 1 to x = 2.
What is 7/3
200
Evaluate
int_-1^3 1/x dx
What is ln(3)
200
Find the integral
int (1/t - 2/t^2)dt
What is
ln|t| + 2/t + C
200
Find the integral
int45e^(0.15x) dx
What is
300e^(0.15x)+C
200
If G'(t) represents the rate at which the number of gallons of gasoline are pumped from a local gas station between days a and b, interpret the meaning of
int_5^10 G'(t)dt
The integral represents the total amount of gasoline pumped from the local gas station between days 5 and 10.
200
Setup an integral to find the area in the image below:
What is 7/2
300
Evaluate
int_4^9(2x + 3sqrt(x))dx
What is 103
300
Find the integral
int (x^(3/2) + 1/5sqrt(x))dx
What is
2/5*x^(5/2) + 2/15*x^(3/2) + 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, for a day in September for the city of San Francisco, in MegaWatts, with t measured in hours starting at midnight. Interpret the meaning of
int_0^24 P'(t)dt
What is total amount of MegaWatts used in the day.
300
Find the are of the region bounded by
f(x)=x^2-9
, the x-axis, and the vertical lines x = 1 and x = 4.
What is
38/3
400
Evaluate
int_1^2(e^x + 6/x^4)dx
What is
e^2 - e + 7/4
400
Evaluate:
int_0^2 10e^(-5x)dx
What is
400
A company's financial analyst is advising the management that an investment in new technology will save it money at the rate of
S'(t)=4,000(1-0.07e^(-0.07t))
dollars per month t months after the purchase of the new technology.
The analyst advised the management that if it purchases the new technology, it will save, through the next 24 months, just over $100,000. As a manager, would you accept or reject the analyst's claim? Explain.
The savings over the next 24 months are $92,746, so the analyst's claim is too high. It should be rejected.
400
Find the area completely enclosed by
f(x)=2-x^2
and
g(x)=x
What is 9/2 or 4.5
500
Evaluate
int_0^1 x/(1 + 5x^2)dx
What is ln(6/10)
500
Find the exact area of the shaded region shown below:
What is 23/2