11/17/14, 2:15 PMMath 125 HW_1CPage 2 of 152.6/6 points | Previous AnswersSCalcET7 5.2.004.(a) Find the Riemann sum for with six terms, taking the sample points tobe right endpoints. (Round your answers to six decimal places.)R6= 2.776802 2.776802(b) Repeat part (a) with midpoints as the sample points.M6= 5.130861 5.130861Solution or ExplanationClick to View Solution3.6/6 points | Previous AnswersSCalcET7 5.2.007.A table of values of an increasing function fis shown. Use the table to find lower and upper estimates for lower estimate -76 -76upper estimate 16 16x10141822 26 309Solution or ExplanationClick to View Solutionf(x) = 5 sin x, 0 ≤x≤3π/2,f(x) dx.3010f(x)−14−9−114
11/17/14, 2:15 PMMath 125 HW_1CPage 3 of 154.5/5 points | Previous AnswersSCalcET7 5.2.009.Use the Midpoint Rulewith the given value of nto approximate the integral. Round the answer to fourdecimal places.-3.0484 -3.0484Solution or Explanationso the endpoints are 0, 14, 28, 42, and 56, and the midpoints are 7, 21, 35, and49. The Midpoint Rule gives sin dx, n= 456x0Δx= (56 −0)/4 = 14,sin dx≈56x4f(xi)Δx= 14(sin+ sin+ sin+ sin) ≈14(−0.2177) = −3.0484.i= 172135490
11/17/14, 2:15 PMMath 125 HW_1CPage 4 of 155.5/5 points | Previous AnswersSCalcET7 5.2.017.MI.Express the limit as a definite integral on the given interval.Master ItExpress the limit as a definite integral on the given interval.Part 1 of 2On the interval [a, b], the limit gives us the integralFor we have Solution or ExplanationClick to View Solution6.9/9 points | Previous AnswersSCalcET7 5.2.034.MI.The graph of gconsists of two straight lines and a semicircle. Use it to evaluate each integral.lim n→∞nxiln(1 + xi2) Δx, [2, 6]i= 1dx62lim n→∞nxiln(1 + xi4)Δx, [1, 4]i= 1lim n→∞nf(xi)Δxi= 1.f(x) dxbaΔx,lim n→∞nxiln(1 + xi4)i= 1f(x) = (No Response).
11/17/14, 2:15 PMMath 125 HW_1CPage 5 of 15(a) Master ItThe graph of g(x) consists of two straight lines and a semicircle. Use it to evaluate the integral.g(x) dx100g(x) dx80
11/17/14, 2:15 PMMath 125 HW_1CPage 6 of 15Step 1 of 2If g(x) is positive, then the integral corresponds to the area beneath g(x) and above the x-axis over the interval [a, b].On [0, 8], the function g(x) is above the x-axis and is therefore positive. Thus, equals thearea of the triangle created by the function, the x-axis, and the y-axis.This triangle is a right triangle with a side length of (No Response)8along the x-axis and a sidelength of (No Response)16along the y-axis. (Give the numeric values.) (b) Master ItThe graph of g(x) consists of two straight lines and a semicircle. Use it to evaluate the integral.Step 1 of 3On the interval the graph is a semi-circle. Since the semi-circle is below the x-axis, then is the negative of the area of this semi-circle. The radius of this semi-circle is (Give the numeric value.) g(x) dxbag(x) dx80g(x) dx3010g(x) dx248[8, 24],g(x) dx248r= (No Response)8.