5-6 Find the area of the shaded region by (a) integrating with respect to x and (b) integrating with respect to y. 5. y 6. y = 2x (2,4) /y=x² 2 X 5 2² = 4x ((1, -2) (4,4) y=2x-4 5 x
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- Sketch the region enclosed by y = e 3 x y = e 3 x , y = e 8 x y = e 8 x , and x = 1 x = 1 . Decide whether to integrate with respect to x x or y y . Then find the area of the region.15) Sketch the region of integration and evaluate the integral:∫30∫√9−x20(x3+xy2)dy dx17. Region bounded by y = 2x, y = x and x = 2. Rotate about: (a) the y-axis (b) x = 2 (c) the x-axis (d) y = 4
- Show complete solution (with graph). 1. Determine the centroid of the area bounded by the y − axis, the x − axis, and the curve x^2 + y − 4 = 0.Sketch the region enclosed by y=e^4x, y=e^9x , and x=1x=1. Decide whether to integrate with respect to xx or yy. Then find the area of the region.SOLVE STEP BY STEP IN DIGITAL FORMAT Determine the centroid of the region bounded by the curves: y=sin(x), y=Φ; x=π /4 : x=3π /4
- Solve the problem with complete solution and draw the figure. Determine the ordinate of the centroid of the area bounded by the curve x2 = 8y and the line 2x – y = 0.find the absolute maximum and minimum values of ƒ on the region R. ƒ(x, y) = x2 - y2 - 2x + 4y R: The triangular region bounded below by the x-axis, above by the line y = x + 2, and on the right by the line x = 2.find the absolute maximum and minimum values of ƒ on the region R. ƒ(x, y) = 4xy - x4 - y4 + 16 R: The triangular region bounded below by the line y = -2, above by the line y = x, and on the right by the line x = 2.
- Evaluate triple integration of xz *dv with respect to E where E is the solid tetrahedron with vertices (0,0,0),(0,1,0),(1,1,0) and (0,1,1)In Exercises 1–4, sketch the region bounded by the given lines and curves. Then express the region’s area as an iterated double integral and evaluate the integral. 1. The curves y = ln x and y = 2 ln x and the line x = e, in the first quadrant 2. The parabolas x = y2 and x = 2y - y2 3. The parabolas x = y2 - 1 and x = 2y2 - 2 4. The lines y = x, y = x/3, and y =2.Sketch the region enclosed by y=e^3x ,y=e^8x, and x=1. Decide whether to integrate with respect to x or y, and then find the area of the region.