Question

Find antiderivative 5x-x^(1/2)
How come on the -x side the answer is 2x^(3/2) / 3 ? Does the 3/2 get flipped when it goes to the bottom?

Answer 1

Because
\[ \frac{1}{3/2} = \frac{2}{3} \]

Answer 2

I wish I knew its bad retricethough, I think its a monkey eagle or vietnam eagle

Answer 3

Ok james so I don't just take the exponent and add one to it then put it on the bottom I actually have to take the exponent over 1?

Answer 4

Remember that the antiderivative of \( x^n, n \neq 1 \) is
\[ \frac{1}{n+1}x^{n+1} \ \ (+ C) \]

In this case,y ou want the antiderivative of \( x^{1/2} \), hence n = 1/2. Using the rule just written down, we have n = 1/2 and thus the antiderivative is
\[ \frac{1}{1+ 1/2} x^{1 + 1/2} = \frac{1}{3/2} x^{3/2} = \frac{2}{3} x^{3/2} \]

Answer 5

if I take x^2 for example, its an easy x^(3) / 3

Answer 6

Yes

Answer 7

thanks JamesJ!