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Integration Intuition

When calculating areas, it’s a good idea to check your answer against a rough visual estimate of the region’s area. For each graph shown below, select the value that’s closest to the shaded area.

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Integration Intuition

When calculating areas, it’s a good idea to check your answer against a rough visual estimate of the region’s area. For each graph shown below, select the value that’s closest to the shaded area.

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Integration Intuition

When calculating areas, it’s a good idea to check your answer against a rough visual estimate of the region’s area. For each graph shown below, select the value that’s closest to the shaded area.

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Summation

Compute the following sums:

  • \sum_{k=1}^{5}k^{2}

    #Just write down the final value

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Summation

Compute the following sums:

  • \sum_{k=1}^{3}(2k)^{2}

    # Just write the final value

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Summation

Compute the following sums:

  • \sum_{n=1}^{4}(-1)^{n}n

    # Just right down the final value

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Summation

Compute the following sums:

  • \sum_{k=0}^{5}2^{k}

    #Just right down the final value

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Integral of |x|

  • Use the geometric definition of the definite integral to compute: 

    \int_{-1}^{2} |x|dx

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Riemann Sum Practice ▼Math Symbols ▲Math Symbols

Common forms and functions
  • x+y x+y
  • x·yx*y
  • x/yx÷y
  • xyx**y
  • √xsqrt(x)
  • x!factorial(x)
  • ln(x)log(x)
  • exexp(x)
  • log10(x)log(x, 10)
  • log2(x)log(x, 2)
  • sin(x)sin(x)
  • cos(x)cos(x)
  • tan(x)tan(x)
  • cot(x)1/tan(x)
  • atan(x)atan(x)
  • asin(x)asin(x)
  • acos(x)acos(x)
  • sinh(x)sinh(x)
  • cosh(x)cosh(x)
  • tanh(x)tanh(x)
  • eE
  • πpi
  • Use a Riemann sum with n = 6 subdivisions to estimate the value of \int_{0}^{2} (3x+2)dx

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Massachusetts Institute Of Technology
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View the complete course at: http://ocw.mit.edu/18-01F06

Lecture 17 is Exam 2, so no video was recorded.

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