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Complete the following steps for the given function, interval, and value of $n.$a. Sketch the graph of the function on the given interval.b. Calculate $\Delta x$ and the grid points $x_{0}, x_{1}, \ldots, x_{n}$c. Illustrate the midpoint Riemann sum by sketching the appropriate rectangles.d. Calculate the midpoint Riemann sum.$$f(x)=\sqrt{x} \text { on }[1,3] ; n=4$$

(a) graph (b) $?x = \dfrac{1}{2};1\dfrac{2}{3}2,\dfrac{2}{5},3$(c)graph (d)2.80

Calculus 1 / AB

Calculus 2 / BC

Chapter 5

Integration

Section 1

Approximating Areas under Curves

Integrals

Integration Techniques

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Yeah. Okay, so we're ask defined area under the careers of vaccine equals square root of X on 13 a. M and use it for sub generals. So on left here, I've got my little sketch of affects equals Vertex Delta X. The length of each sub interval is thievery in. So three minutes one divided by the number of sub intervals for J equals 0.5 x bar. One is Thea Average is the midpoint of the first Southerner bull, which is the average of beginning in the end of the sub in a rule. Um, so zeros one x one is 1.5. So we take the average of those we got 1.25 and then for the rest of the X Barbara how use we can add Delta X delayed, sir. Venerable to expire one in order to to get these values. So next in part, C were asked to sketch the midpoint Riemann sons, which I've done here and then lastly were asked to find the midpoint. Riemann some. So here you use our formula so f of x bar, one blood fx bar two plus f of expert three possessive X bar four all times fills the X. And so we get our values for that's bar one from, um, from our function after that clip was Rex. So if X borrow one is the sweat rude of 1.25 as of X, part two is the square root of 1.7 fucking. And so once we had all those up by by the defects, which is your 15 and then you will get our answer, which is ultimately to point.

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