Question

Find the area of the region between y=x^1/3 and y=x^1/5 for 0 less than or equal to x less than or equal to 1.

Answer 1

\[\int_0^1(x^{\frac{1}{3}}-x^{\frac{2}{5}})dx\]

Answer 2

How do you find the antiderivative of a fraction?

Answer 3

Just add one to it and take the reciprocal

Answer 4

So it would be 3x^4/3 and 5x^6/5

Answer 5

We know the reciprocal of 4/3 is 3/4, but you only have the 3. You are close, but it should be:
\[(3/4)x ^{4/3}-(5/7)x ^{7/5}\] and evaluate in the given interval

Answer 6

o duh right thanks!

Answer 7

Wait, I was going off of Satellites. It is 6/5, not 7/5

Answer 8

ya i figured that. Thanks for the help!