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In this lesson, we will learn how to find and compare the areas under the curves of functions using the Riemann sum.

Q1:

Suppose that πΉ β² ( π₯ ) = 3 ο± ο ο‘ and πΉ ( 0 ) = 7 . Find two estimates of πΉ ( 1 ) to three decimal places using the left and then the right endpoint methods with 8 rectangles.

Q2:

Calculate the midpoint rule estimate of οΈ π₯ + 2 π₯ 4 0 2 d with π = 2 subintervals. Is the result an overestimate or underestimate of the actual value?

Q3:

Calculate the right endpoint estimate of οΈ π₯ + 2 π₯ 4 0 2 d with π = 2 subintervals. Is the result an overestimate or underestimate of the actual value?

Q4:

The table gives sampled values of an increasing function π . Use the data to give a lower and upper bound for οΈ π ( π₯ ) π₯ ο¨ ο« ο§ ο¦ d .

Q5:

The table gives sampled values of an increasing function π . Use the data to give a lower and upper bound for οΈ π ( π₯ ) π₯ ο¨ ο¨ ο§ ο¨ d .

Q6:

Calculate the left endpoint estimate of οΈ π₯ + 2 π₯ 4 0 2 d with π = 2 subintervals. Is the result an overestimate or underestimate of the actual value?

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