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- Evaluate each of the double integrals in Exercises 41–44 asiterated integrals. 41.∬Rsin(x + 2y) dA,where R = {(x, y) | 0 ≤ x ≤ π and 0 ≤ y ≤ π/2}42.∬Rx sin x cos y dA,where R = {(x, y) | −3 ≤ x ≤ 2 and −2 ≤ y ≤ 2}43.∬Rxexy dA,where R = {(x, y) | 0 ≤ x ≤ 1 and 0 ≤ y ≤ ln 5}44.∬Rx2 cos(xy) dA,where R = {(x, y) | 0 ≤ x ≤ π and 0 ≤ y ≤ 1}Use Fubini's theorem to solve the double integral provided in the first image. R is the triangle [-1,2] x [0,2].Evalute the attached integral Using: a) Multiple-application trapezoidal rule n = 2 and n = 4 b) Single application of Simpson's 1/3 rule
- 1. Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1, y=2 xdy+ydx=3xdx 2. Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1, y=1 x^2(xdy+ydx)=8xdy-8ydxSay that you need to compute a double integral of the function f(x,y)=xy over the region D bounded by the x-axis, y=x, x2+y2=1, and x2+y2=16. Explain in words and/or show in a picture why this would be (unnecessarily) complicated in Cartesian coordinates. Then, setup and evaluate the integral using polar coordinates.Let f(x,y)=x2ex2f(x,y)=x2ex2 and let RR be the triangle bounded by the lines x=3x=3, x=y/2x=y/2, and y=xy=x in the xyxy-plane. (a) Express ∫RfdA∫RfdA as a double integral in two different ways by filling in the values for the integrals below. (For one of these it will be necessary to write the double integral as a sum of two integrals, as indicated; for the other, it can be written as a single integral.)
- How can I solve this integral if R is the solid bounded by z=3x, z=x^2, y=0, and y=2? How do I write the bounds and the function?How would you evaluate the double integral of a continuous function ƒ(x, y) over the region R in the xy-plane enclosed by the tri-angle with vertices (0, 1), (2, 0), and (1, 2)? Give reasons for your answer.Use the substitution formula to evaluate the integral. the integral from 0 to 1 (8y^2-y+1)^-1/3 (32y-2) dy show all work