First of all, surely you can simplify ...
Hi everyone, I have the following problem: What is the solid formed by rotating the region bounded by y=ln(x+1),x=0,y=2 around the y axis? The answer would be its pi/2(e^4-4e^2+7). How would one solve this problem? Would one find the intersection of y=2 and y=ln(x+1) which i got to be ((e^2)-1,ln(e^2)) and then take the integral of ln(x+1) from o to (e^2)-1 away from the area under y=2 from o to (e^2)-1 to get formula the cross section and then to find the volume integrate the formula for the cross section squared (radius) from y=0 to 2 and then times by pi?
Is this correct?
No, for an arbitrary disk, the radius is found by extending from the y-axis to the x-coordinate on the logarithmic curve.
Look at the graph I provided and picture an arbitrary horizontal line in the shaded area serving as the radius of some disk.