Sketch the area between two curves and then find the area. This is using summations.

y=2x^{1/3}, y=(1/8)x^{2}, 0<=x<=6

So I got the sketch okay, but I feel I am making some mistake somewhere in the algebraish part.

IGNORE THIS WORK! CHECK THE COMMENTS. I posted a new version with the right integration and still got the wrong answer. Look at that!

1. Subtract the bottom curve from the other. [2x^{1/3}-(1/8)x^{2}]

2. Get the antiderivtive. [(3/4)(2x^{4/3})-(1/24x^{3})]=[6/4x^{4/}^{3}-(1/24)x^{3}]

3. Plug the values 6 and 0 in and solve

[(6/4)(6^{4/3})-(1/24)(6^{3})]-[(6/4)(0^{4/3})-(1/24)(0^{3})]

=[(6/4)(6^{4/3})-9]-0

The book says the answer is (47/3)-[(9/2)(12^{1/3}) which is between 5 and 6. However, when I plug the value above into a calculator, I get between 7 and 8. Where am I going wrong?

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