Given the graph of the function f(x) below, use a right Riemann sum with 4 rectangles to approximate the area under the curve over the interval [2, 6]. 13 12 11 10 9. 8 7 6. 4 3 1. 4. 5. 6. LO
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- Expand/Write out (but do NOT calculate) the Riemann sum, Rs, for the function f(x) = 1 - |x| on the interval [-1,14]. Use the function explicitly.Consider the function f(x) = x2The goal is to find a general formula for the area under this curve onthe interval [0, b]. (a) Start by looking at finding the area under the graph of f(x) on [0, 1] using N rectangles, using the right endpoints as the test points. What do the endpoints look like? Use this to write the approximate area in summation notation. (b) What if this is done on [0, 2], still using N rectangles? How does this change the formulas and the sum? What are the right endpoints here? (c) What if this also done on [0, b] for some positive number b using N rectangles? What are the endpoints here? (d) With this last sum, expand things out and use the power sum rules to get this to an expression only depending on N. (e) Take the limit as N → ∞ to get the area under the graph of f(x) over [0, b].Evaluate the Riemann sum for f(x) = x3 − 6x + 2, taking the sample points to be midpoint and a = 0, b = 4, and n = 8b) Find the exact value of ∫03 f(x) dx using Riemann sum c) Find the exact value of ∫03 f(x) dx using the Fundamental Theorem of Calculus
- A) Calculate the left Riemann sum for the given function over the given interval, using the given value of n. (When rounding, round your answer to four decimal places. If using the tabular method, values of the function in the table should be accurate to at least five decimal places.) HINT [See Example 2.] f(x) = 39 − 117x over [−1, 1], n = 4The following function is positive and negative on the given interval. f(x)=9-x2; [0,4] a. Sketch the function on the given interval. b. Approximate the net area bounded by the graph of f and the x-axis on the interval using a left, right, and midpoint Riemann sum with n=4 c. Use the sketch in part (a) to show which intervals of [0,4] make positive and negative contributions to the net area.