Calculating the Left Riemann Sum Approximation for ∫101f(x)ⅆx Using Four Subintervals

The continuous function f is known to be increasing for all x. Selected values of f are given in the table above. Let L be the left Riemann sum approximation for ∫101f(x)ⅆx using the four subintervals indicated by the table. Which of the following statements is true

To find the left Riemann sum approximation for ∫101f(x)ⅆx using the four subintervals, we need to calculate the area of rectangles formed by the function values and the width of the subintervals

To find the left Riemann sum approximation for ∫101f(x)ⅆx using the four subintervals, we need to calculate the area of rectangles formed by the function values and the width of the subintervals.

Looking at the table, we have the following information:

Subinterval [1, 2]:
f(1) = 3

Subinterval [2, 4]:
f(2) = 5
f(4) = 7

Subinterval [4, 7]:
f(4) = 7
f(7) = 10

Subinterval [7, 10]:
f(7) = 10
f(10) = 11

Now, let’s calculate the left Riemann sum approximation:

For the subinterval [1, 2], we take the leftmost value f(1) = 3.
The width of the subinterval is 2 – 1 = 1.
Therefore, the area of this rectangle is 3 * 1 = 3.

For the subinterval [2, 4], we take the leftmost value f(2) = 5.
The width of the subinterval is 4 – 2 = 2.
Therefore, the area of this rectangle is 5 * 2 = 10.

For the subinterval [4, 7], we take the leftmost value f(4) = 7.
The width of the subinterval is 7 – 4 = 3.
Therefore, the area of this rectangle is 7 * 3 = 21.

For the subinterval [7, 10], we take the leftmost value f(7) = 10.
The width of the subinterval is 10 – 7 = 3.
Therefore, the area of this rectangle is 10 * 3 = 30.

Finally, we add up the areas of all the rectangles to find the left Riemann sum approximation:
L = 3 + 10 + 21 + 30 = 64.

Therefore, the true statement is that the left Riemann sum approximation for ∫101f(x)ⅆx using the four subintervals is equal to 64.

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