Hello, I would like to make sure the answers to these questions are correct.
1. Using the shell method, what is the volume of a solid that is generated by rotating the region by y = x^2 and x = y^2 about the x axis.
My Work:
r = y
h = sqrt(y) - y^2
2pi ∫[0,1] (y)((sqrt(y) - y^2))dy
My Answer: 2pi (1^2/2)((1^(3/2)/(3/2))-1^3/3)
= pi/3
2. Using the shell method, what is the volume of a solid that is generated by rotating the region in the first quadrant bounded by the curve y = sqrt(x^2+1) and x = sqrt(3) about the y axis?
My Work: r = x
h = sqrt(x^2+1)
2pi ∫[0,sqrt(3)] (x)(sqrt(x^2+1))dx
My Answer (sqrt(3)^3)/3)+(sqrt(3)^2/2)
= 20.307
I would really appreciate if you could let me know if these answers are correct. I am trying to practice this stuff and I want to make sure I am practicing correctly! Thank You!!
1 answer