need to get the concept down...

**winterwyrm** · November 17th 2007, 02:07 PM

Evaluate the integral.

**bobak** · November 17th 2007, 02:26 PM

Okay I'm going to have to assume you know how to deal with expression in the form of $\int_{}^{}{ae^{bx}}dx$ If you don't just say.

Now to integrate $3^x$ we just need to rewrite it as e raised to an particular power, consider $y = 3^x$ then $ln(y) = ln(3^x) .... ln(y) = xln(3)$ now we just antilog both sides so $y = e^{xln3}$

so you understand how to write $3^x$ as $e^{xln3}$

so to integrate you just use the chain rule backwards $\int_{}^{}{e^{xln3}}dx = \frac{e^{xln3}}{ln3} = \frac{3^{x}}{ln3}$

now in general $\int{a^x} dx = \frac{a^x}{lna}$

**winterwyrm** · November 17th 2007, 03:33 PM

cool response, but it doesnt work.... F(3)-F(1) isnt' the right answer.....

**Krizalid** · November 17th 2007, 03:50 PM

$(a^x)'=(e^{x\ln a})'=a^x\ln a.$

Integrate both sides

$a^x+k_1=\int a^x\ln a\,dx\,\therefore\,\frac{a^x}{\ln a}+k=\int a^x\,dx.$

So $\int_1^33^x\,dx=\left.\frac{3^x}{\ln3}\right|_1^3$

What's the problem with this?

**winterwyrm** · November 17th 2007, 07:26 PM

I get 21.84 when I plug that in, and when I try to submit it for my online homework..... I get a red X (I have a hundred submissions though)..... is this a serious problem?

**Jhevon** · November 17th 2007, 08:17 PM

Originally Posted by winterwyrm

I get 21.84 when I plug that in, and when I try to submit it for my online homework..... I get a red X (I have a hundred submissions though)..... is this a serious problem?

can't you enter exact answers? or does the system accept decimal approximations? (it would be 21.85 to two decimal places)

**winterwyrm** · November 17th 2007, 09:09 PM

its wrong... 22, 22.9, 21.85, even 21, and 23....

**Jhevon** · November 17th 2007, 09:16 PM

Originally Posted by winterwyrm

its wrong... 22, 22.9, 21.85, even 21, and 23....

check again to see if you wrote the right question, because i see nothing wrong with the responses given. did you try typing in 24/(ln 3)? this is definately the right answer for the question asked

**winterwyrm** · November 17th 2007, 09:23 PM

that worked! THanks so much!! I was so confused!!

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