dr Consider the integral I = The approximation of I by using the Ji V5 - 2 composite Trapezoidal rule with n 4 subintervals is: (a) 0.6527 (b) 0.6522 (c) 0.6322 (d) 0.5527
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Solved in 2 steps
- a) Express the integral as a Riemann sum.b) Graphf x( )then draw and shade the right endpoint rectangles, ? = 4, that estimate the bounded by f x( )and the x-axis on the given interval.c) Approximate the area of the shaded region by using the Midpoint Rule with n = 4.FIND THE CENTROID OF THE REGION IN THE FIRST QUADRANT BOUNDED BY THE GRAPH OF y=9-x2, THE X-AXIS, AND THE Y-AXIS (SOLVE BY USING INTEGRAL CALCULUS)Q1:- Find the area bounded by the curve F(X)=(-X^2)+8X-7 and the x-axis between the function’s x-intercepts using a Riemann sum. Use of the Fundamental Theorem of Calculus without a Riemann sum will be awarded no credit.
- Evalute the attached integral Using: a) Multiple-application trapezoidal rule n = 2 and n = 4 b) Single application of Simpson's 1/3 ruleFind the area of the region under the graph of the function f on the interval [5, 11], using the Fundamental Theorem of Calculus. Then verify your result using geometry. f(x) = 9 How many square units?Estimate the area of the region bounded bythe graph of ƒ(x) = x2 + 2 and the x-axis on [0, 2] in the followingways.Divide [0, 2] into n = 4 subintervals and approximate the areaof the region using a right Riemann sum. Illustrate the solutiongeometrically.
- a. Use the Trapezoidal Rule to approximate the integral. (Round to four decimal places.) b. Estimate the error in using the approximation. Express the answer rounded to three decimal places. c. Determine the number n of subintervals needed to guarantee that an approximation is correct to within 0.0001Using the left-endpoint Riemann sum with 4 equal subintervals, estimate the area of the region bounded above by the curve f(x) = ex + e-x and below by the x-axis, on the interval [−1, 3]. Provide answer with three decimal places.Approximation the integral (formula attached) using sinpson’s rule with ? = 4 subintervals.
- Evaluate the triple integral XYZdV The bounds of the integrals is the the tetrahedron with vertices (0, 0, 0), (0, 1, 0), (1, 1, 0), and (0, 1, 1).A CAT scan produces equally spaced cross-sectional views of a human organ that provide information about the organ otherwise obtained only by surgery. Suppose that a CAT scan of a human liver shows cross-sections spaced 1.5 cm apart. The liver is 15 cm long and the cross-sectional areas, in square centimeters, are 0, 17, 58, 77, 95, 107, 118, 127, 63, 39, and 0. Use the Midpoint Rule with n = 5 to estimate the volume V of the liver.Using Simpson’s Rule with n=2 subintervals, evaluate the integral 3∫1lnxdx. Round the answer to 3 decimal places.