(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

f(x)=kx^{2}+x^{3}, where is k is a positive constant. Let R be the region in the first quadrant bounded by the graph of F and the x-axis.

a. Find all values of the constant k for which the area of R equals 2.

b. For k>0, write an integral expression in terms of k for the volume of the solid generated when R is rotated around x-axis.

c. For k>0, write an expression in terms of k, involving one or more integrals, that gives the perimeter of R.

2. Relevant equations

V= pi *r^{2}

3. The attempt at a solution

a. For a. I find the interception of F(x) and the x-axis. After that, I set up an integral of f(x) evaluating from 0 to k and set that integral equal to 2. Am I right.

b. and c. I don't really get the part of in terms of k. so I just do a normal integration of dish method of f(x) and I substitute the number in part a for k. Am I right ? Or is it trickier ?

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# Homework Help: A volume problem

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