Question

Integrate!

Answer 1

\[\displaystyle \int\limits_0^1 8^{3 x}\, dx\]

Answer 2

lny = 3xln8

Answer 3

Use the property
\[\Huge \int\limits a^x = \frac{a^x}{\log a}\]

Answer 4

(8^x)/log8 ?

Answer 5

Put 3x=t

Answer 6

So it becomes,
\[\Huge \frac{1}{2}\int\limits_0^\frac{1}{2} 8^t dt\]
Now shoot the property.

Answer 7

sorry that would be 1/3 , i thought its 2x

Answer 8

yeah

Answer 9

\[\Huge \frac{1}{3}\int\limits\limits_0^\frac{1}{3} 8^t dt\]
Can you do now?

Answer 10

so then we get 8^t /(log8*3) eval at 1/3

Answer 11

no thats wrong >.>

Answer 12

oh snap, i know what i did

Answer 13

\[\Large \frac{1}{3} \frac{8^t}{\log 8}]_0^\frac{1}{3}\]

Answer 14

\[\Large \frac{1}{3} (\frac{2}{\log 8} - \frac{1}{\log 8})=> \frac{1}{3 \log 8}\]

Answer 15

woah where did 2 -1 come from?

Answer 16

\[\Huge 8^\frac{1}{3} = (2)^{3 \times \frac{1}{3}}\]

Answer 17

and 8^0=1

Answer 18

there we go, thats what i was missing... i was just dropping off the whole second part of the integral

Answer 19

thank you

Answer 20

haha be careful next time :)

Answer 21

yeah the -1/log8 got me!

Answer 22

@DLS we were still wrong it was evaluated at 3 and 0, instead of 1/3 and 0 the answer wasn't accepting so i redid it :p