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#8 The table gives the values of a function obtained from an experiment. Use them to estimate (integral sign with 9 at top and 3 at bottom) f(x) dx using three equal subintervals with a) right endpoints, b) left endpoints, c)midpoints. If the function is known to be an increasing function, can you say whether your estimates are less than or greater than the exact value of the integral?

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Answers:

Pilly

Oracle

Karma Points: 24,080

Date Posted: 5/29/2008 10:47:38 PM Status: Live

Asker's Rating: Lifesaver

Response:

A) using right endpoints

The width of each rectangle will be 2 units. Heights will be f(5), f(7), f(9)

1st rectangle area will be (2)(-0.6)

2nd rectangle area will be (2)(0.9)

3rd rectangle are will be (2)(1.8)

Total area using right endpoints = (-1.2 + 1.8 + 3.6) = 4.2

For B) use widths of 2 units and left endpoint heights of f(3), f(5), f(7)

For C) use widths of 2 units and midpoint heights of f(4), f(6), f(8)

af_boy_18's Comment:

Thanks!

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Integrals

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