Applications Of Definite Integrals Series
10 Questions
| Total Attempts: 748
(161).jpg "Applications Of Definite Integrals Series")
Integrals can be used to measure a lot of phenomena that affect us in our everyday life. We've set up a series of exercise to help you conceptualize and practice this section of mathematics. Complete this quiz and see if you understand all the principles behind them.
Questions and Answers
- 1.
![By approximately how many micromoles does the plasma concentration increase between x=x=1100x, equals, 100 and x=200x, equals, 200? - ProProfs]( "By approximately how many micromoles does the plasma concentration increase between x=x=1100x, equals, 100 and x=200x, equals, 200?")
By approximately how many micromoles does the plasma concentration increase between x=x=1100x, equals, 100 and x=200x, equals, 200?- A.
0.067
- B.
0.15
- C.
7.42
- D.
33.5
- 2.
![The depth of the water in Harsha's bird bath is changing at a rate of r(t)=0.25t-0.1r(t)=0.25t−0.1r, left parenthesis, t, right parenthesis, equals, 0, point, 25, t, minus, 0, poin millimeters per hour (where tt is the time in hours). At time t=t=0t, equals, 0, the depth of the water is 353535 millimeters. What is the depth of the water at t=t3t, equals, hours? - ProProfs]( "The depth of the water in Harsha's bird bath is changing at a rate of r(t)=0.25t-0.1r(t)=0.25t−0.1r, left parenthesis, t, right parenthesis, equals, 0, point, 25, t, minus, 0, poin millimeters per hour (where tt is the time in hours). At time t=t=0t, equals, 0, the depth of the water is 353535 millimeters. What is the depth of the water at t=t3t, equals, hours?")
The depth of the water in Harsha's bird bath is changing at a rate of r(t)=0.25t-0.1r(t)=0.25t−0.1r, left parenthesis, t, right parenthesis, equals, 0, point, 25, t, minus, 0, poin millimeters per hour (where tt is the time in hours). At time t=t=0t, equals, 0, the depth of the water is 353535 millimeters. What is the depth of the water at t=t3t, equals, hours?- A.
35+∫33r(t)dt
- B.
35+∫34r(t)dt
- C.
35+∫23r(t)dt
- D.
35+∫03r(t)dt
- 3.
![The velocity of a particle moving along the xxx-axis is v(t)=3v(t)=3t+2v, left parenthesis, t, right parenthesis, equals, 3, t, plus, 2. At t=0t=0t, equals, 0, its position is 33.
What is the position of the particle, ss(t)s, left parenthesis, t, right parenthesis, at any time ttt? - ProProfs]( "The velocity of a particle moving along the xxx-axis is v(t)=3v(t)=3t+2v, left parenthesis, t, right parenthesis, equals, 3, t, plus, 2. At t=0t=0t, equals, 0, its position is 33.
What is the position of the particle, ss(t)s, left parenthesis, t, right parenthesis, at any time ttt?")
The velocity of a particle moving along the xxx-axis is v(t)=3v(t)=3t+2v, left parenthesis, t, right parenthesis, equals, 3, t, plus, 2. At t=0t=0t, equals, 0, its position is 33. What is the position of the particle, ss(t)s, left parenthesis, t, right parenthesis, at any time ttt?- A.
S(t)=3
- B.
S(t)=3t2+2t+3
- C.
S(t)=2/3t2+2t
- D.
S(t)=2/3t2+2t+3
- 4.
![It takes 505050 minutes for Joe to notice that his cola bottling machine has sprung a leak. Joe is able to stop the leak in 1010 minutes. The graph below shows the rate at which cola leaks from the machine as a function of time.
How much cola does Joe lose in this bottling disaster? - ProProfs]( "It takes 505050 minutes for Joe to notice that his cola bottling machine has sprung a leak. Joe is able to stop the leak in 1010 minutes. The graph below shows the rate at which cola leaks from the machine as a function of time.
How much cola does Joe lose in this bottling disaster?")
It takes 505050 minutes for Joe to notice that his cola bottling machine has sprung a leak. Joe is able to stop the leak in 1010 minutes. The graph below shows the rate at which cola leaks from the machine as a function of time. How much cola does Joe lose in this bottling disaster?- A.
300
- B.
200
- C.
490
- D.
100
- 5.
![The cumulative profit a business has earned is changing at a rate of r(t)r(t)r, left parenthesis, t, right parenthesis dollars per day (where ttt is the time in days). In the first 3030 days, the business earned a cumulative profit of $1700dollar sign, 1700.
What does 1700+∫3090r(t)dt1700+\displaystyle\int_{30}^{90}r(t)\,dt1700+∫3090r(t)dt1700, plus, integral, start subscript, 30, end subscript, start superscript, 90, end superscript, r, left parenthesis, t, right parenthesis, space, d, t represent? - ProProfs]( "The cumulative profit a business has earned is changing at a rate of r(t)r(t)r, left parenthesis, t, right parenthesis dollars per day (where ttt is the time in days). In the first 3030 days, the business earned a cumulative profit of $1700dollar sign, 1700.
What does 1700+∫3090r(t)dt1700+\displaystyle\int_{30}^{90}r(t)\,dt1700+∫3090r(t)dt1700, plus, integral, start subscript, 30, end subscript, start superscript, 90, end superscript, r, left parenthesis, t, right parenthesis, space, d, t represent?")
The cumulative profit a business has earned is changing at a rate of r(t)r(t)r, left parenthesis, t, right parenthesis dollars per day (where ttt is the time in days). In the first 3030 days, the business earned a cumulative profit of $1700dollar sign, 1700. What does 1700+∫3090r(t)dt1700+\displaystyle\int_{30}^{90}r(t)\,dt1700+∫3090r(t)dt1700, plus, integral, start subscript, 30, end subscript, start superscript, 90, end superscript, r, left parenthesis, t, right parenthesis, space, d, t represent?- A.
The rate at which the cumulative profit was increasing when t=90.
- B.
The change in the cumulative profit between days 30 and 90
- C.
The cumulative profit the business has earned as of day is 90
- D.
The time it takes for the cumulative profit to increase another 1700 after the first 30 days
- 6.
![Jackson received the following problem:
A particle moves in a straight line with velocity v(t)=6t−20v(t)=6t-20v, left parenthesis, t, right parenthesis, equals, 6, t, minus, 2 meters per second, where tttt is time in seconds. At t=1t, equals, 1, the particle's distance from the starting point was 99 meters in the positive direction. What is the particle's position at t=4t=4t, equals, 4 seconds?
Which expression should Jackson use to solve the problem? - ProProfs]( "Jackson received the following problem:
A particle moves in a straight line with velocity v(t)=6t−20v(t)=6t-20v, left parenthesis, t, right parenthesis, equals, 6, t, minus, 2 meters per second, where tttt is time in seconds. At t=1t, equals, 1, the particle's distance from the starting point was 99 meters in the positive direction. What is the particle's position at t=4t=4t, equals, 4 seconds?
Which expression should Jackson use to solve the problem?")
Jackson received the following problem: A particle moves in a straight line with velocity v(t)=6t−20v(t)=6t-20v, left parenthesis, t, right parenthesis, equals, 6, t, minus, 2 meters per second, where tttt is time in seconds. At t=1t, equals, 1, the particle's distance from the starting point was 99 meters in the positive direction. What is the particle's position at t=4t=4t, equals, 4 seconds? Which expression should Jackson use to solve the problem?- A.
9+∫1 4v′(t)dt
- B.
∫14v′(t)dt
- C.
9+∫14v(t)dt
- D.
∫14v(t)dt
- 7.
![What is the area of the region enclosed by the graphs of f(x)=x2+2x+11f(x)=x^2+2x+11f, left parenthesis, x, right parenthesis, equals, x, start superscript, 2, end superscript, plus, 2, x, plus, 11 , g(x)=−4x+2g, left parenthesis, x, right parenthesis, equals, minus, 4, x, , and x=x=0x, equals, 0? - ProProfs]( "What is the area of the region enclosed by the graphs of f(x)=x2+2x+11f(x)=x^2+2x+11f, left parenthesis, x, right parenthesis, equals, x, start superscript, 2, end superscript, plus, 2, x, plus, 11 , g(x)=−4x+2g, left parenthesis, x, right parenthesis, equals, minus, 4, x, , and x=x=0x, equals, 0?")
What is the area of the region enclosed by the graphs of f(x)=x2+2x+11f(x)=x^2+2x+11f, left parenthesis, x, right parenthesis, equals, x, start superscript, 2, end superscript, plus, 2, x, plus, 11 , g(x)=−4x+2g, left parenthesis, x, right parenthesis, equals, minus, 4, x, , and x=x=0x, equals, 0?- A.
21
- B.
6
- C.
9
- D.
63
- 8.
![What is the area of the region between the graphs of f(x)=8x+6f(x)=8x+6f, left parenthesis, x, right parenthesis, equals, 8, x, plus, 6 and g(x)=x−x2g(x)=x-x^2, g, left parenthesis, x, right parenthesis, equals, x, minus, x, start superscript, 2, end sup, from x=−6x, equals, minus to x=−1x=-1x, equals, minus, 1 ? - ProProfs]( "What is the area of the region between the graphs of f(x)=8x+6f(x)=8x+6f, left parenthesis, x, right parenthesis, equals, 8, x, plus, 6 and g(x)=x−x2g(x)=x-x^2, g, left parenthesis, x, right parenthesis, equals, x, minus, x, start superscript, 2, end sup, from x=−6x, equals, minus to x=−1x=-1x, equals, minus, 1 ?")
What is the area of the region between the graphs of f(x)=8x+6f(x)=8x+6f, left parenthesis, x, right parenthesis, equals, 8, x, plus, 6 and g(x)=x−x2g(x)=x-x^2, g, left parenthesis, x, right parenthesis, equals, x, minus, x, start superscript, 2, end sup, from x=−6x, equals, minus to x=−1x=-1x, equals, minus, 1 ?- A.
485/6
- B.
643/6
- C.
1195/6
- D.
125/6
- 9.
![A region is enclosed by the yyy-axis, the line y=1yy, equals, 1, and the curve y=x3y=x^3y, equals, x, start superscript, 3, end superscri.
What is the volume of the solid generated when this region is rotated around the xx-axis? - ProProfs]( "A region is enclosed by the yyy-axis, the line y=1yy, equals, 1, and the curve y=x3y=x^3y, equals, x, start superscript, 3, end superscri.
What is the volume of the solid generated when this region is rotated around the xx-axis?")
A region is enclosed by the yyy-axis, the line y=1yy, equals, 1, and the curve y=x3y=x^3y, equals, x, start superscript, 3, end superscri. What is the volume of the solid generated when this region is rotated around the xx-axis?- A.
6.33
- B.
5
- C.
0.67
- D.
6π/7
- 10.
![The base of a solid SS is the region bounded by the circle x2+y2=16x^2+y^2=16x, start superscript, 2, end superscript, plus, y, start superscript, 2, end superscript, equals, 16. Cross-sections perpendicular to the xx-axis are rectangles with heights twice as large as their bases.
Determine the exact volume of solid SSS. - ProProfs]( "The base of a solid SS is the region bounded by the circle x2+y2=16x^2+y^2=16x, start superscript, 2, end superscript, plus, y, start superscript, 2, end superscript, equals, 16. Cross-sections perpendicular to the xx-axis are rectangles with heights twice as large as their bases.
Determine the exact volume of solid SSS.")
The base of a solid SS is the region bounded by the circle x2+y2=16x^2+y^2=16x, start superscript, 2, end superscript, plus, y, start superscript, 2, end superscript, equals, 16. Cross-sections perpendicular to the xx-axis are rectangles with heights twice as large as their bases. Determine the exact volume of solid SSS.- A.
2048/3
- B.
2048/4
- C.
148/3
- D.
148/4
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