Question

int_{}^{}10^x dx =
integrate it.
if can show me the step please.

Answer 1

since your missing the ln(10) id find a suitable "1" to use on it

Answer 2

the value not needed. i just need the way to solve it. the notes given by my lecturer is incomplete.=(

Answer 3

10^x comes from a: 10^x

but when we derivative it we get: 10^x ln(10)

the ln(10) is just a constant so we can borrow it from a "1". ln(10)/ln(10) is a good "1" to use

Answer 4

its either that or fill you mind with all the u sub stuff for something so generic :)

Answer 5

u = 10^x

du = 10^x ln(10) dx

du/ln(10) = 10^x dx

int: du/ln(10)

Answer 6

\[\int 10^x\ dx\]
\[\int 1*10^x\ dx\]
\[\int \frac{ln(10)}{ln(10)}*10^x\ dx\]
\[\frac{1}{ln(10)}\int ln(10)*10^x\ dx\]

Answer 7

the 10^x dx need to sub it with dy/ln10 ?

Answer 8

need to? no. Can you? sure ...

Answer 9

then the final answer is??

Answer 10

\[\int 10^x\ dx\]
\begin{array}l
u=10^x\\
du=10^x\ ln(10)\ dx\\
\frac{1}{ln(10)}du=10^x\ dx
\end{array}
\[\int\frac{1}{ln(10)}du\]
\[\frac{1}{ln(10)}\int\ du\]

Answer 11

the final answer is what you get to when you finish off the integration :)

Answer 12

is the final answer 1/ln(10) * 10^x ?

Answer 13

yep, sure is; +C if your doing the indefinite integral

Answer 14

ok... so if i did not sub the with the 1/ ln(10), would the answer still the same?

Answer 15

It must be the same.

Answer 16

there is only one answer ....

Answer 17

there are many methods to get there; but only one answer

Answer 18

ok...i understand it now.thanks a lot.=)

Answer 19

youre welcome

Answer 20

You can generalize this problem. It is true for all a > 0 that
\[ \frac{d \ }{dx} a^x = \ln a \ . a^x \]
Hence
\[ \int a^x \ dx = \frac{1}{\ln a} a^x \ + C \]

Answer 21

Notice when a = e, than ln a = ln e = 1, hence
\[ \int e^x = e^x + C \]
which is what we expect.