Calculate this and get a FullInfoAccount

[blubb12345]

it seems that nobody is able to do/understand it, so here's a picture how the graph with the right a looks like



SOLVED

This is how I did it:

[ad1das]

a = 1 (filler)

[blubb12345]

a = 1 (filler)

wrong (fillingfillfiller)

[camicio]

a=0.69314718055994530941723212145818
passes through (0.5,0)

Not sure what you mean to be honest.

[TwistedPixel]

x=1
whoohoo!!!

[blubb12345]

2. wrong
3. wrong

[camicio]

Wait, I'm stupid.
a=0.34657359027997265470861606072909
passes through (1/sqrt(2),0)

[EatUrBrains]

lol it is f(x)=1/x

[wow4Supplier]

a= (1 . 1)

EDIT: I mean X coordinate 1,y coordinate 1

[blubb12345]

still no right answer

[ToR]

My girlfriend's guess is 0 :P

[Cryde]

Wuergh i'm stupid at Maths but I love peter Fox and I'm german too gief !
No srsly it's something like 0,3 ...

[Illidan_000]

Aww.. must think about it I will edit my post later and tell ya

[ReidE96]

Find a value of a such that the area beneath the curve is 0.5
Area beneath f(x) is integral of f(x)
Integral of f(x) = integral of ln(x) + ax +c
=xlnx + ax + c - integral of 1
=xlnx +(a-1)x + c

Upper limit is 1 always, lower limit is... hmmm....

1ln(1) + a - 1 - (xlnx + (a-1)x) = 0.5
a - xlnx - ax + x = 1.5
a(1-x) = 1.5 + x(lnx - 1) = (1.5 + x(lnx-1))/(1-x)

Find the lower limit of x, plug it in, get your answer!

Edit: Thought a little more.

Lower limit is where f(x) = 0 so
ln(x) = -a
x = 1/(e^a)

1ln(1) + a - 1 - (-a/(e^a) + (a-1)/(e^a)) = 0.5
a + a/(e^a) - (a-1)/(e^a) = 1.5
a + e^-a = 1.5
a + 1/(e^a) = 1.5
ae^a + 1 = 1.5e^a
(a - 1.5)e^a = -1

Yeah, I cba now, dinner's ready Enjoy folks!

Edit again: Back from dinner, and seeing as noone has it yet I'll push on.

a + e^-a = 1.5
e^-a = 1.5 - a

We know ln(x) + a = 0 at x = e^(-a)
But we also know e^(-a) = 1.5 - a
So ln(1.5 - a) + a = 0
ln(1.5)/ln(a) = -a
ln(1.5) = -aln(a)
ln(1.5) = ln(a^-a)
a^-a = 1.5
a^a = 2/3

Ok, that's just great.

Lemme try again, from (a - 1.5)e^a = -1
ln of both sides: ln((a-1.5)e^a) = -1
ln(a-1.5) + ln(e^a) = -1
ln(a-1.5) = -a - 1
a = 1.5 + e^(-a - 1)
a = 1.5 + (e^-a)/(e^-1)
a = 1.5 + (e^1)/(e^a)
a = 1.5 + e*e^(-a)

But e^-a = 1.5 - a, so

a = 1.5 + e(1.5 - a)
a = 1.5(1+e) - ea
a(1+e) = 1.5(1+e)
a = 1.5

WOO! Now, common sense tells me something's wrong there. But I don't care

[camicio]

You have to solve
1.5=exp(-a)+a