Help!!!! Need answers asap?

Question

hey, I cannot do this last question, any help really appreciated:

Find the area between the curve y=e (power x) + 1/x and the x-axis and the lines x=1 and x=e.

Give answer exactly, as an expression involving e.

Thank you

Answer 1

Integrate the function from 1 to e

e^x integrates to e^x so between 1 and e is e^e-e
between 1 and e, ln x integrates to 1.

add the two together and you get e^e -e +1

Answer 2

I will translate your given expression:

f(x)=exp(x) + 1/x

(Remember that exp(x) is the same thing that saying e to the power of x)

You are asking for the integral of f(x) computed from x=1 and x=e
(being Int = the symbol of integral):

Int(exp(x) + 1/x) =
Int(exp(x)) + Int(1/x) = exp(x) + ln(x) from x=1 to x=e
exp(e)-exp(1) + ln(e)-ln(1) = exp(e)-e+1-0 =
exp(e) - e

In your notation would be: Area = e^e - e

That´s it!

Good luck!

Answer 3

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