Question

find the area of the region

Answer 1

\[\int\limits_{0}^{7} 8x * \sqrt[3]{x +1} dx\]

Answer 2

Let \(u=x+1\) might work.

Answer 3

try \(u=x+1\)

Answer 4

do I just integrate like normal? These questions always konfuse me :P

Answer 5

then \(x=u-1\) so you get
\[8\int (u-1)\sqrt{u}du\]

Answer 6

to the power of 3.

Answer 7

actually it would be
\[8\int(u-1)\sqrt[3]{u}du\]

Answer 8

Then expand and integrate normally.

Answer 9

when i try to solve, someone has done! -.-

Answer 10

\[8\left(\int u^{\frac{4}{3}}-\int u^{\frac{1}{3}}du\right)\]etc

Answer 11

\[\int\limits \frac{3u^{7/3}}{7} -\int\limits \frac{3u^{4/3}}{4} \] ???

Answer 12

err * 8 :P so 24

Answer 13

+c of course :)

Answer 14

When you integrate the integral is not there; you can't just leave the integral like that.

Answer 15

yeah sorry I messed up lol :P Is the rest of it correct? :)

Answer 16

and change u into x+1... SO that's the area of the region?

Answer 17

I dont think so its suppose to be\[\frac{24u^{\frac{7}{3}}}{7} -6u^{\frac{4}{3}} +C\]

Answer 18

yup that's what I got if i multiplied by 8 which I forgo to :P. So that's the area?

Answer 19

Remmember to sub in the \(x+1\) and don't forget the limits.

Answer 20

\[\frac{24(x+1)^{7/3}}{7} - 6(x-1)^{4/3} 0-7\]

Answer 21

Hm, why did you add the \(0\) out of no where?

Answer 22

Thos ewere my limits sorry.

Answer 23

\[\frac{24(7+1)^{7/3}}{7} - 6(7-1)^{4/3}\] =\[\frac{24(8)^{7/3}}{7} - 6(6)^{4/3}\] = \[\frac{3072}{7} - 6(6)^{4/3}\] which I'm not sure what the fractin is of that...

Answer 24

6^(4/3) is 10.90272355699284

Answer 25

It looks as though you subbed in the limits right. The other part is just simple. :)

Answer 26

Yeah I'm konfused :(

Answer 27

Why so?

Answer 28

I'm stuck at how to figure out the 6(6)^(3/4) Idk how to get it as a fraction, or what do i do?

Answer 29

You can leave it as fractions. It depends on the question. But I don't really like decimals. :)

Answer 30

but what is the fractin of it?

Answer 31

I cannot get a fraction out of 65.4123128

Answer 32

so it's 3072/7 - ???? :(

Answer 33

6^(4/3) = 10.90272355699284 * 6 = 65.41634134195704

Answer 34

Apparently 373.441 should be the decimal answer?

Answer 35

Sorry, I dont have a calculator with me.

Answer 36

http://web2.0calc.com/

Answer 37

oh woops it's 6(x+1) huh...

Answer 38

so 96 is the other answer...

Answer 39

However; http://www.wolframalpha.com/input/?i=integrate+8x%28x%2B1%29%5E%281%2F3%29+from+7+to+0
iif you want verify your answer. (:

Answer 40

Yeah thanks, I really messed up lol :(. Did 6(x-1) instead of x+1 I was wondering aobut that lol.. 96 * 7 / 7
3072/7 - that :)