Question

Find the value of c such that ∫_0^c e^-2x dx=1/4

Answer 1

First, you would want to evaluate\(\displaystyle\int_0^ce^{-2x}~\mathbb dx \).

Try using u-substitution.

Answer 2

Let \(u = -2x\)

Answer 3

Can you handle it? @SARCO06

Answer 4

Not actually, I'm kind of lost

Answer 5

Please help me, is my last question

Answer 6

Alright, so since \(u = -2x\), we have \(\mathbb du = -2\mathbb dx\quad\Longrightarrow\quad -\dfrac{1}{2}\mathbb du = \mathbb dx\), right?

So make substitutions and you have \(\displaystyle\int_0^c -\dfrac{1}{2}e^{u}~\mathbb du =-\dfrac{1}{2}\int_0^c e^{u}~\mathbb du \).

Now can you evaluate \(\displaystyle -\dfrac{1}{2}\int_0^c e^{u}~\mathbb du \)?

Answer 7

Are you still lost? Where are you stuck on?

Answer 8

Yes, I'm lost, I'm trying to evaluate the value of c, but I'm also working on another homework

Answer 9

Are you still there?

Answer 10

\(\large \displaystyle \int_0^c e^u\mathbb du ~~=~~ \left.e^u\phantom{\dfrac{}{}}\right|_0^c~~=~~\left.e^{-2x}\phantom{\dfrac{}{}}\right|_0^c = (e^{-2c})-(e^0)\)

Correct?

Answer 11

Yes, but what's c finally?

Answer 12

Sorry, but I don't get it. I have done this function with the values. I never found one of the values before

Answer 13

You have been very kind and patient with me, I really need to finish this homework. I have the rest of it done