Math  /  Calculus

Question```latex Suppose f(x)=x29 f(x) = \frac{x^{2}}{9} .
(a) The rectangles in the graph on the left illustrate a left endpoint Riemann sum for f(x) f(x) on the interval 2x4 2 \leq x \leq 4 . The value of this left endpoint Riemann sum is \square and it is an _________\_\_\_\_\_\_\_\_\_.
(b) The rectangles in the graph on the right illustrate a right endpoint Riemann sum for f(x) f(x) on the interval 2x4 2 \leq x \leq 4 . The value of this right endpoint Riemann sum is \square and it is an _________\_\_\_\_\_\_\_\_\_ \square the area of the region enclosed by y=f(x) y = f(x) , the x x -axis, and the vertical lines x=2 x = 2 and x=4 x = 4 .

Studdy Solution
(a) The left endpoint Riemann sum is 1.75\mathbf{1.75} and it is an **underestimate**. (b) The right endpoint Riemann sum is 2.41666...\mathbf{2.41666...} and it is an **overestimate** of the area.

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