1. area enclosed

the question is to find the area enclosed between the y axis, the line y=10 and the exponential curve using integration.

so first i need to switch the function around. f(x)=2e^x y=2e^x y/2 =e^x im not sure what i do next is correct. i get ln of both sides ln y/2 = ln e^x so

ln y/2 =x ln e ln y/2 =x (1) ln y/2 =x. i dont know how to integrate ln y/2 after this though i would find the definite integral of from 10 to 2.

2. Re: area enclosed

You're making this more difficult than it isn't ...

The curve intersects the line at $x=\ln{5}$, the upper limit of integration.

Area is just the integral of the upper function minus the lower function ...

$\displaystyle A = \int_0^{\ln{5}} 10-2e^x \, dx$

Evaluate ... you should get $A=10\ln{5}-8$

3. Re: area enclosed

i dont see you get that. i get 10ln5-2e^ln5 =10ln5-10

4. Re: area enclosed

$\bigg[10x-2e^x\bigg]_0^{\ln{5}}$

$\left(10\ln{5}-2e^{\ln{5}}\right)-\left(0-2e^0\right)$

note, $e^{\ln{5}}=5$ and $e^0=1$ ...