Question

(FTOC) Evaluate the integral: (x-1)/x^(1/2) dx, [9,1] Answer: -40/3 Me: 12 (x-1)/x^(1/2) dx = (1/2)x^(3/2) - (1/2)x^(1/2) so: [(1/2)(9)^(3/2) - (1/2)(9)^(1/2)] - [(1/2)(1)^(3/2) - (1/2)(1)^(1/2) = [(27/2)-(3/2)] - [0] =12 I must be doing something wrong on doing the (1/2)x^(3/2) - (1/2)x^(1/2) but I cannot figure it out.

Answer 1

\[\huge \int\limits_1^9 \frac{x-1}{x^{1/2}}dx= \int\limits_1^9 \frac{x}{x^{1/2}}-\frac{1}{x^{1/2}}dx\]

Answer 2

\[\huge \int\limits_1^9 x^{1/2}-x^{-1/2}dx\]

Answer 3

Everything look ok so far? :o

Answer 4

ok I can follow the first one

Answer 5

what happened to the x above x^1/2

Answer 6

Remember when you divide terms that have similar bases, you SUBTRACT the exponents :D This is what that should look like.
\[\huge \frac{x^1}{x^{1/2}}=x^{1-\frac{1}{2}}=x^{1/2}\]

Answer 7

duh, yes now both make sense.

Answer 8

ah good c:

Answer 9

\[\frac{ x ^{1/2} + ^ {1} }{ 1 }\]

Answer 10

The equation tool is a little tricky ^^ takes some time to get used to it

Answer 11

Woops, for the power rule of Integration, you raise the power, then divide by the NEW power.
So your new power on the bottom should be 1/2 + 1

Answer 12

\[\huge \int\limits x^n dx = \frac{x^{n+1}}{n+1}\]\[\huge \int\limits x^{1/2}dx=\frac{x^{(1/2+1)}}{1/2+1}\]

Answer 13

so \[\frac{ 3 }{ 2 }(x^{3/2})?\]

Answer 14

We're DIVIDING by 3/2, remember what we do when we divide by a fraction?

Answer 15

Grrrrr ....... Heh it's the Algebra that kills ya.

2/3's

Answer 16

heh c: ya

Answer 17

\[- 2(x^{1/2})\]

Answer 18

for the 2nd part.

Answer 19

Mmmm yah that looks good.

Answer 20

cool .... now plug 9 into both and subtract plugging 1 into both and that should be my new answer.

Answer 21

yah sounds good c:

Answer 22

thanks again.