Question

What is E 2x integral?????


__No Useless Answer Plzzz-_-​

Answer 1

Answer:

$\huge{\sf{\green{a} \blue{n} \pink{s} \purple{w} \green{e} \red{r}}}$

Well , there are a couple of ways , how about this:

Let’s try to solve it using our intuition , we are looking for a function that has a derivative equal to e2xe2x.Well , we know that the derivative of exex gives exex but we are missing the 2 in the exponent .So we try e2xe2x , but it’s derivative is 2∗e2x2∗e2x , no worries we just divide by 2 , so the 2s cancel .So the answer is 12e2x.12e2x.

We can also try a more straight-forward way , using substitution.

We want to solve: ∫e2xdx∫e2xdx ,we will substitute 2x with y,

y=2x,∫eydx,y=2x,∫eydx, but now our variable and our differential are different , so differentiating y=2xy=2x we get , dy=2dxdy=2dx so , dx=dy2,dx=dy2,substituting we have , ∫12eydy∫12eydy, the 1212 can go outside the integral as it is a constant , so finally,

Step-by-step explanation:

No Useless Answer @Chudail G.

Answer 2

Step-by-step explanation:

It is

1

2

e

2

x

.

You can certainly use the technique of integration by substitution (reversing the chain rule) to find this, you can also reason as follows:

The antiderivative of

e

2

x

is a function whose derivative is

e

2

x

.

But we know some things about derivatives at this point of the course. Among other things, we know that the derivative of

e

to a power is

e

to the power times the derivative of the power.

So we know that the drivative of

e

2

x

is

e

2

x

⋅

2

. That's twice a big as what we want.

We also know that constant factors just hang out in front when we take derivatives, so if we stick a

1

2

out front, it will be there after we differentiate and we can cancel the two.

f

(

x

)

=

1

2

e

2

x

has

f

'

(

x

)

=

e

2

x

so it is an antiderivative. The general antiderivative then is

1

2

e

2

x

+

C

is the answer correct ?