1. Consider the function f(x) = x - 4 on the interval [-2,2]. Calculate the Riemann sum using: a. n=6, right endpoints b. n=4, midpoints c. Evaluate x -4 dx -2 d. Which estimate of the area, "a" or "", is closer to the actual area, "c"?

Q: Consider the function f(x) = 4x2 −x3. Provide the graph of the region bounded by f(x) and the x-axis…

A: The solution is given below in the next step:

Q: 4. Let f(x) = 4x22/3-19x71/11 Determine the largest n for which f E C". %3D

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Q: Find the area enclosed by the graphs of a = f(y) = y³ - 26y + 10 and x = g(y) = 40 - 6y² - y³. (a)…

A: Given:The functions are  and To Find:(a) The intersection point(b) Functions that are to the right…

Q: 4. Find the exact area using the Riemann sum for f(x) = 6x² - 4 on the interval [2,5]

A:

Q: Estimate the area under the graph (sqr-root):x+4 over the interval [-4,12] using 8 approxiamating…

A: Given function: Width of each interval = (12-(-4))/8= 16/8= 2  So the partition is -4, -2, 0, 2, 4,…

Q: Approximate the area under graph (a) of f(x)=1/x over the interval [2,10] by computing the area of…

A: In this question, the approximate area of rectangles is determined.

Q: Use the definition of area as a Riemann sum (as we did in Section 4.4) to compute the area between…

A: The area under the curve over the interval  is  Here

Q: Find the area under the graph of y = 2x² - 2x + 4 on the interval [-2,0].

A: y=2x2−2x+4 on the interval [−2,0]

Q: 6. Fill in the blank: The length of the graph of y = x² on [2, 4] is equal to the area under the…

A: y=x2 on the interval 2, 4. Differentiating with respect to x, we get dydx=2x Now length of the curve…

Q: naled by a patient's lungs. Suppose Figure 1, below, shows the rate of exhalation for a rticular…

A:

Q: Use rectangles to estimate the area under the graph of ƒ(x) = 4 − x², above the x-axis and from x =…

A:

Q: Estimate the area under the graph of f(1) = over the interval [-2, 3] using ten approximating | I +…

A: The given function is fx=1x+4 over the interval -2,3 using ten approximating rectangles. Calculate…

Q: Find the area under the curve of the following function f(x) = 7x³ on the interval [2, 6].

A: Given a function,f(x)=7x3To find: The area under the curve on the interval [2,6]

Q: Partition [0,pi] into four equal partsand calculate the lower and upper sums for g(x)=2sinx.  What…

A: The Left Riemann Sum (also Left Endpoint Approximation) uses the left endpoints of a sub interval:

Q: Use the Riemann Sum to find the area of the region bounded by the graph of f(x)=tan(x/6) and the…

A: Sol:- Given function, f (x) =Tanx6 , x -axis, x∈[o,2π]area bounded by given curves = ∫02π Tanx6dxlet…