Integration (1 Viewer)

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yeyjasminetime

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Hi,

Find y as a function of x, if y' = 1/4x and y= 1 and y = 1 when x = e2. What is the x intercept of this curve?

If someone could explain this to me, it would be great. Thank you.
 
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HeroicPandas

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When y = 1, x = e2 (is this e squared? im gonna assume its e squared)



Therefore y = .......

What is an x-intercept? It is when the curve cuts the x-axis, so the y-coordinate must be...?
 
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yeyjasminetime

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Yes! That's where I got up to. The x intercept is when y = 0. I'm just confused about what C is and what it's got to do with anything?

Thanks heroic panda :)
 
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HeroicPandas

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the reason why u have 'C' is that the original function could have a constant added to it

eg. y = x+1, y' = 1
If u integrate back, u get:
y = x + C

eg. y = x, y' = 1
If u integrate back, u get:
y = x + C

C is determined by a relation between x and y

Another example, y' = x^2 /2
Integrate with respect to x
y = x + C
U dont know if the original function could have been y = x+2 or y = x+ 223 or y = x + 2013, etc

THats why the C is there
 
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HeroicPandas

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x-intercept occurs when y = 0,

So we let y = 0,



Make 'lnx' the subject and put it on the left so its easier to see,



(THIS PART, changing logs to exponential, DO U UNDERSTAND?)
 
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yeyjasminetime

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THATS EXACTLY THE PART I DONT UNDERSTAND! I think I should revise my log and Ln. My teacher said to use Ln instead of log.

:/
 
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