Applications Of Definite Integrals Series

10 Questions | Total Attempts: 748

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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?
    • 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?
    • A. 

      35+∫​3​3​​r(t)dt

    • B. 

      35+∫​3​4​​r(t)dt

    • C. 

      35+∫​2​3​​r(t)dt

    • D. 

      35+∫​0​3​​r(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?
    • A. 

      S(t)=3

    • B. 

      S(t)=3t​2​​+2t+3

    • C. 

      S(t)=​2/​​3​​t​2​​+2t

    • D. 

      S(t)=​2​​/3​​t​2​​+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?
    • 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+∫​30​90​​r(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?
    • A. 

      9+∫​1​ 4​​v​′​​(t)dt

    • B. 

      ∫​1​4​​v​′​​(t)dt

    • C. 

      9+∫​1​4​​v(t)dt

    • D. 

      ∫​1​4​​v(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?
    • 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 ?
    • 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^3​​​y, 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.
    • A. 

      2048/3

    • B. 

      2048/4

    • C. 

      148/3

    • D. 

      148/4

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