Evaluate the integrals in Exercises 17–66. V3 – 2s ds 17. 18. ds V5s + 4 fovT 20. / 3y V7 – 3y² dy 19. 1 ·J Vx(1+ Vx}* - dx sin x cos³ x dx 21. 22.
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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}Evaluate the double integral of cos(x) with x from 0 to π/4 and y from 4y to πCalculate the double integral. ∫∫ ey ^2 dA, D= {(x,y)| 0≤ y ≤3, 0≤ x ≤ y}
- Evaluate the triple integral. E 8x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the plane x = 5Evaluate the triple integral, 4x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the plane x = 5.Evaluate the triple integralE 7xdV, where E is bounded by the paraboloid x = 7y2 + 7z2 and the plane x = 7.
- Evaluate the triple integralSSSE Sin y dV, where E lies below the plane z= x and above the triangular region with the vertices (0,0,0), (π,0,0) and (0,π,0)Find the general integral and compute 3 diferent solutions for : xzx+(x+z)zy=y-xEvaluate the triple integral ∭ExdV where E is the solid bounded by the paraboloid x=9y2+9z2and x=9.