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In this lesson, we will learn how to find an approximated value of the area under a curve using midpoint approximation.

Q1:

Let π ( π₯ ) = 5 4 π₯ over 1 β€ π₯ β€ 2 . Using four subintervals and taking midpoints as sample points, evaluate the Riemann sum of π to six decimal places.

Q2:

Let π ( π₯ ) = 1 5 π₯ over 1 β€ π₯ β€ 5 . Using four subintervals and taking midpoints as sample points, evaluate the Riemann sum of π to six decimal places.

Q3:

Using the midpoint rule with π = 5 , round οΈ 2 π₯ 3 π₯ + 2 π₯ 5 2 d to four decimal places.

Q4:

Using the midpoint rule with π = 5 , round οΈ 3 π₯ 2 π₯ β 5 π₯ 4 3 d to four decimal places.

Q5:

The table shows the values of a function obtained from an experiment. Estimate οΈ π ( π₯ ) π₯ 7 1 d using three equal subintervals with midpoints.

Q6:

The table shows the values of a function obtained from an experiment. Estimate οΈ π ( π₯ ) π₯ 1 9 1 d using three equal subintervals with midpoints.

Q7:

The table shows the values of a function obtained from an experiment. Estimate οΈ π ( π₯ ) π₯ 2 5 1 d using three equal subintervals with midpoints.

Q8:

The table shows the values of a function obtained from an experiment. Estimate οΈ π ( π₯ ) π₯ 1 0 4 d using three equal subintervals with midpoints.

Q9:

Estimate οΈ 5 ο» 2 β 3 π₯ ο π₯ 9 1 s i n d using the midpoint rule with π = 4 , giving your answer to four decimal places.

Q10:

Estimate using the midpoint rule with , giving your answer to four decimal places.

Q11:

Q12:

Using the Midpoint Rule with π = 5 , give an estimate of οΈ 5 β 2 π₯ + 1 π₯ 1 0 3 d . Give your answer to four decimal places.

Q13:

Given π ( π₯ ) = π₯ β 4 2 and β 4 β€ π₯ β€ 2 , evaluate the Riemann sum for π with six subintervals, taking sample points to be midpoints.

Q14:

Given π ( π₯ ) = 2 π₯ β 4 2 and β 1 β€ π₯ β€ 5 , evaluate the Riemann sum for π with six subintervals, taking sample points to be midpoints.

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