Mathematics, 08.10.2019 14:20 lakeithiat1320

Iwould like to know if my answers are correct: disclaimer: we are allowed to keep our answers in formula form
1. use the washer method to find the volume of the solid that is generated by rotating the plane region bounded by y=x^2 and y = 2-x^2 about the axis y=-1
my work: [pi((3-(1))^2+1)^2] - [pi(())^2+1)^2
my 0? ? 2. use the washer method to find the volume of the solid that is generated by revolving the region bounded by the lines 3y = 2x, x=0, and y=2 about the y-axis
my work: pi(9(2)^3/12) my 72pi/12 3. use the washer method to find the volume of the solid that is generated by rotating the region in the first quadrant bounded above by y = cosx and on the right x = pi/2 about the line y=2
my work: pi((4(pi/2) - ((2-(cos(pi/2))^3)/3) my 11.36 4. use the washer method to find the volume of the solid that is generated by revolving the region bounded by the curve y-x^3, y=0, and x=2 about the x-axis
my work: pi(2^4/4) my answer = 4pi i would greatly appreciate if you could let me know if my answer are correct. i am trying to practice as much as i can, and i would really like to know if i am understanding the material correctly. if the answer if wrong i would really appreciate if you could give me a clue as to where i can try to start to solve the problem.

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