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Definite Integrals

Definite Integrals

Example 1

Let R be the region between the graph y = f ( x ) = x2 + 1 and the x-axis on the interval [0,4]:

Use a left-hand sum with two sub-intervals to approximate the area of R.

Example 2

Let R be the region between the graph y = f ( x ) = x2 + 1 and the x-axis on the interval [0,4]. Use a Left-Hand Sum with 4 sub-intervals to estimate the area of R.

Example 3

Let S be the region between the graph of g and the x-axis on the interval [0,4].

Use a left-hand sum with 2 sub-intervals to estimate the area of S. Is this an under-estimate or an over-estimate?

Example 4

  • Let W be the region between the graph of f and the x-axis on the interval [-20,20].

Use a left-hand sum with 4 sub-intervals to estimate the area of W.

  • Let Z be the region between the graph of g and the x-axis on the interval [-4,0].
    LHS graphs 4 - without pink
  • Use a left-hand sum with 2 sub-intervals to estimate the area of Z.
  • Use a left-hand sum with 4 sub-intervals to estimate the area of Z.

Example 5

Let f ( x ) = x2 + 2 and let R be the region between the graph of f and the x-axis on the interval [0,8]. Use a left-hand sum with 4 sub-intervals to estimate the area of R.

Example 6

Let f ( x ) = 4x and let R be the region between the graph of f and the x-axis on the interval [1,2]. Use a left-hand sum with 4 sub-intervals to estimate the area of R.

Example 7

Let f ( x ) = 2x on [2,10]. Find LHS(5). That is, use a left-hand sum with 5 sub-intervals to estimate the area between the graph of f and the x-axis on [2,10].

Example 8

Use a left-hand sum to estimate the area between the graph of g and the x-axis on the interval [0,10].

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