Accumulation & Riemann Sums Assessment Test

10 Questions | Total Attempts: 105

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Accumulation & Riemann Sums Assessment Test

Accumulation and Riemann sums are used when the definite integral represents the area under the curve of a function between two vertical lines but we can't go find this area easily, so we can estimate it using simpler shapes like rectangles.


Questions and Answers
  • 1. 
    Integrate ∫ 3x+2 dx from x=1 to x=4.
    • A. 

      28.5

    • B. 

      28.6

    • C. 

      28

    • D. 

      28.7

  • 2. 
    Approximate the area under the curve of ∫ cos(x) dx from x=1 to x=5.
    • A. 

      -3.14

    • B. 

      3.14

    • C. 

      -1.8004

    • D. 

      1.8004

  • 3. 
    Integrate f(x)= x^3+4 from x=-2 to x=2 using left riemann sums with four equal subintervals. 
    • A. 

      6

    • B. 

      7

    • C. 

      8

    • D. 

      9

  • 4. 
    Integrate and solve ∫ cos(x) dx from x=-11 to x=4.
    • A. 

      3.14

    • B. 

      -1.757

    • C. 

      -3.14

    • D. 

      4.12

  • 5. 
    Integrate and solve ∫ 2x-cosx dx from x=1 to x=6.
    • A. 

      36.121

    • B. 

      24.75

    • C. 

      -36.121

    • D. 

      -24.75

  • 6. 
    Integrate and solve ∫ cos x dx from x=π to x=3π.
    • A. 

      0

    • B. 

      1

    • C. 

      2

    • D. 

      3

  • 7. 
    Integrate and solve ∫1/x +2 dx from x=2 to x=5.
    • A. 

      1n (5/2) +6

    • B. 

      -1n (5/2) +6

    • C. 

      1n (3) +2

    • D. 

      -1n (3) +2

  • 8. 
    Integrate and solve ∫-sin(x)^2-cos(x) from x=12 to x=12.
    • A. 

      -2

    • B. 

      -1

    • C. 

      0

    • D. 

      1

  • 9. 
    Integrate and solve ∫3x^5 dx from x=-5 to x=1.
    • A. 

      -42

    • B. 

      42

    • C. 

      7821

    • D. 

      -7821

  • 10. 
    Integrate and solve ∫2x dx from intervals x=1 to x=3.
    • A. 

      -12

    • B. 

      12

    • C. 

      -8

    • D. 

      8