Having trouble with this Calc 2 problem:
1. Consider the solid whose base is the region enclosed by the curves y=3sinx and y=sinx whose cross-sections, taken perpendicular to the base and parallel to the y-axis, are squares.
Using the general slicing method, formulate an equation that gives the volume of a representative slice.
1. Consider the solid whose base is the region enclosed by the curves y=3sinx and y=sinx whose cross-sections, taken perpendicular to the base and parallel to the y-axis, are squares.
Using the general slicing method, formulate an equation that gives the volume of a representative slice.
-
Note that 3 sin x = sin x ==> sin x = 0 ==> x = 0 to π are the endpoints of the region.
A cross-section will have edge length 3 sin x - sin x = 2 sin x.
So, the area (being a square) equals (2 sin x)^2 = 4 sin^2(x).
So, the volume equals ∫(x = 0 to π) 4 sin^2(x) dx.
I hope this helps!
A cross-section will have edge length 3 sin x - sin x = 2 sin x.
So, the area (being a square) equals (2 sin x)^2 = 4 sin^2(x).
So, the volume equals ∫(x = 0 to π) 4 sin^2(x) dx.
I hope this helps!