Question

f(x)=e(x/2)-2
calculat the area bounded to f, the x-axis and the line x = 4

Answer 1

Hello again.

Answer 2

Ok I understand the question but I also need to know the bounds of the area.... so the top and bottom will be x-axis and the function... but what about the left and right sides?

Answer 3

x=4 and x=?

Answer 4

(in order right and left)

Answer 5

well it is not given in the problem, but the domain = real numbers

Answer 6

Well as I mentioned before f(x) has an asymptote of x=-2 so the area to the left of the y-axis is -infinity.... so this implies the left bound on x should be x=0...however I only suggested that the bound is the zero of f(x) because the first part of the question had us find it.

Answer 7

Implies it should be x=0 because if the domain is all the reals then the integral of the function from -infinity to 4 = -infinity

Answer 8

Im assuming this is a calculus class yes?

Answer 9

When you have done problems like this before... did you ever calculate negative area? By this I mean did you ever calculate the area UNDER the x-axis? If not then the bounds should be 2 ln(2) (the zero of the function) to 4 since here the area is strictly positive. Otherwise from x=0 to x=2 ln(2) the area is finite but negative (i.e. the curve is UNDER the x-axis not above)

Answer 10

If you havent already... look: http://www.wolframalpha.com/input/?i=graph+the+function+e%5E%28x%2F2%29+-+2+from+x%3D-5+to+x%3D5

Answer 11

Check the other examples in your textbooks and see what they do. Do they ever have a curve BELOW the x-axis and have you calculate that area? Or is it ALWAYS area ABOVE the x-axis? (btw please note my caps are only meant to emphasize the important words)

Answer 12

can i contact you if i have problems that cannot solve in the future

Answer 13

sure if I am on I will help.. but what about the above questions? This a calculus class, correct? What did the other examples in your textbook do?

Answer 14

yes it is. it caculate only above x-axies

Answer 15

Ok brilliant

Answer 16

The area under a curve is given by the integral of the function between the bounds

Answer 17

So we are looking for:
\[ \int_{2 \ln(2)}^4 (e^{\frac{x}{2}} - 2 ) dx \]

Answer 18

Do you know the anti-derivative of the exponential function?

Answer 19

yes

Answer 20

BTW hello @misty1212 your drawing is far better than any I have ever done here.... hence why I try to avoid them XD

Answer 21

Ok then mayada please calculate and post the anti-derivative of:
\[e^{\frac{x}{2}}-2\] and we will compare answers :D

Answer 22

lol thanks!

Answer 23

:D

Answer 24

Thanx misty1212 :) PlasmaFuzer it will be Integration by Parts right?

Answer 25

No fortunately we can do this in one go... no by-parts is necessary.

Answer 26

So for the function:
\[f(x)=e^{ax}\]The anti-derivative is:
\[F(x)=\frac{e^{ax}}{a}\]

Answer 27

This website has all of a sudden become EXTREMELY laggy (facepalms) this is really frustrating

Answer 28

lol

Answer 29

I typed those in 10 seconds... took 2 minutes for the text to display and to post and for me to regain control of the text box.

Answer 30

I have the same problem here. so iam not the only one :P

Answer 31

XD yes you are not alone... my advice would be to type in a text editor and cut and paste into the box... So back to the problem... what did you calculate the anti-derivative of the function to be?