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Using a finite sum to estimate the average value of f on the given interval by partitioning the interval into four subintervals of equal length and evaluating f at the subinterval midpoints.
F(t)=13.5+sin2(pi×t) on [8,10]
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- a) Find the average value of 1/x on the closed interval [1,3]. b) Evaluate the integral of2/sqrt (1 -x²) dx from 0 to 1/2. c) Evaluate the integral of 5x/sqrt (1 + x²) dx with limits from 0 to 3.Using the definition of the definite integral ( infinite Riemann Sum), find the area under the curvef(x) = 3x2 on the interval [0,1]Using a Riemann sum with right endpoints and n=4 subintervals, estimate the area under the graph of f(x)=sin(x) from x=0 to x=pi
- Use a Riemann sum to approximate the area under the graph of f(x)=e-x on the interval 0≤x≤1 using n=5 subintervals with the selected points as the right end points. The Area is approximately _________units?Use a finite sum to estimate the average value of f on the given interval by partitioning the interval into four subintervals of equal length and evaluating f at the subinterval midpoints. f(x) = 4/x on [1,17] The average value is_________(simplify your answer)Use a finite sum to estimate the average value of f(x)=3/x on the interval [1,25] by partitioning the interval into four subintervals of equal length and evaluating f at the midpoints of the subintervals. (Saw this done already but it was the wrong answer (8.2431))
- Let f(x) = 4x with the interval [0, 2]. (a) Use a Riemann sum with four subintervals of equal length (n = 4) to approximate the area of R. Choose the representative points to be the right endpoints of the subintervals. (b) Repeat part (b) with eight subintervals of equal length (n = 8).Evaluate the Riemann sum for f(x)= ln(x) -1.5 over the interval [ 1,5] using eight subinterval, taking the sample points to be midpoints.Consider the function f(x) = 4x2 −x3. Provide the graph of the region bounded by f(x) and the x-axis over the interval [0, 4]. Which type of Riemann sum (left or right) gives a better estimate for the area of this region? may use the graphing calculator to facilitate the calculation of the Riemann sum
- (a) Estimate the area under the graph of the function f(x)=1/(x+6) from x=0 to x=3 using a Riemann sum with n=10 subintervals and right endpoints. Round your answer to four decimal places. (b) Estimate the area under the graph of the function f(x)=1/(x+6) from x=0 to x=3 using a Riemann sum with n=10 subintervals and left endpoints. Round your answer to four decimal places.Calculate the left Riemann sum for the given function over the given interval a.) f(x) = 3x2 over [−2, 2], n = 4 b.) f(x) = 8x2 over [1, 5], n = 4Let f(x)=sin x a. Estimate the area under the graph of f(x)=sin x from x=0 to x=pi by partitioning the interval into 4 equal subintervals and finding the associated Riemann sum E (b=4 and a= k=1) f(ck) change of xk, using the right hand endpoint of the ach subinterval as ck in the subinterval. Use the Fundamental Theorem of Calculus , Part 2 to evaluate the integral sign (b=pi and a=0) (sin x)dx.