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

Q1:

Given that π ( π₯ ) = 4 π₯ c o s and that 0 β€ π₯ β€ π 4 , evaluate, to the nearest six decimal places, the Riemann sum for π with six subintervals, taking the sample points to be left endpoints.

Q2:

Given that π ( π₯ ) = π₯ c o s and that 0 β€ π₯ β€ 4 π 3 , evaluate, to the nearest six decimal places, the Riemann sum for π with six subintervals, taking the sample points to be left endpoints.

Q3:

Given that π ( π₯ ) = 4 π₯ c o s and that 0 β€ π₯ β€ 3 π 5 , evaluate, to the nearest six decimal places, the Riemann sum for π with six subintervals, taking the sample points to be left endpoints.

Q4:

Given that π ( π₯ ) = π₯ c o s and that 0 β€ π₯ β€ π 2 , evaluate, to the nearest six decimal places, the Riemann sum for π with six subintervals, taking the sample points to be left endpoints.

Q5:

The table shows the values of a function obtained from an experiment. Estimate οΈ π ( π₯ ) π₯ 1 7 5 d using three equal subintervals with left endpoints.

Q6:

The table shows the values of a function obtained from an experiment. Estimate οΈ π ( π₯ ) π₯ 2 6 2 d using three equal subintervals with left endpoints.

Q7:

The table shows the values of a function obtained from an experiment. Estimate οΈ π ( π₯ ) π₯ 2 7 3 d using three equal subintervals with left endpoints.

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 left endpoints.

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