Hello! I am having trouble with a math problem. Here is the detail:
A solid is enclosed by two cylinders z = x^2 and y = x^2 and two planes y = 4 and z = 0.
Find the volume of this solid.
I was using double integral with integrand = y, and the bounds are y is from x^2 to 4, and x is from -2 to 2, in order of dydx, and got my answer of 128/5, but the textbook shows 128/15.
Could anyone please help me see if I was doing wrong somewhere or the textbook is wrong? Any comment would be greatly appreciated.
A solid is enclosed by two cylinders z = x^2 and y = x^2 and two planes y = 4 and z = 0.
Find the volume of this solid.
I was using double integral with integrand = y, and the bounds are y is from x^2 to 4, and x is from -2 to 2, in order of dydx, and got my answer of 128/5, but the textbook shows 128/15.
Could anyone please help me see if I was doing wrong somewhere or the textbook is wrong? Any comment would be greatly appreciated.
-
V = ∫(x = -2 to 2) ∫(y = x^2 to 4) (x^2 - 0) dy dx
...= ∫(x = -2 to 2) x^2 (4 - x^2) dx
...= 2 ∫(x = 0 to 2) (4x^2 - x^4) dx, since the integrand is even
...= 2(4x^3/3 - x^5/5) {for x = 0 to 2}
...= 128/15.
I hope this helps!
...= ∫(x = -2 to 2) x^2 (4 - x^2) dx
...= 2 ∫(x = 0 to 2) (4x^2 - x^4) dx, since the integrand is even
...= 2(4x^3/3 - x^5/5) {for x = 0 to 2}
...= 128/15.
I hope this helps!