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# Almost correct - what am I doing wrong? C4 substitution integration

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Why bother with a post grad course - waste of time? 17-10-2016
1. Integrate 1/(20-kV) dV

u = 20-kV

du/dV = -k

dV = du/-k

Therefore it becomes

Integrate 1/-ku du

= -k ln(20-kV)

HOWEVER, the answer is actually ln(20-kV)

How is this so? I'd appreciate somebody clarifying, thank you in advance.
2. (Original post by hopefuldentist10)
Integrate 1/(20-kV) dV

u = 20-kV

du/dV = -k

dV = du/-k

Therefore it becomes

Integrate 1/-ku du

= -k ln(20-kV)

HOWEVER, the answer is actually ln(20-kV)

How is this so? I'd appreciate somebody clarifying, thank you in advance.
Note that: .
3. (Original post by hopefuldentist10)
Integrate 1/(20-kV) dV

u = 20-kV

du/dV = -k

dV = du/-k

Therefore it becomes

Integrate 1/-ku du

= -k ln(20-kV)

HOWEVER, the answer is actually ln(20-kV)

How is this so? I'd appreciate somebody clarifying, thank you in advance.
In this is instance, K just represents a constant. When you integrate a constant with respect to x, you make no changes to the constant itself.

You can re-write the integral as I = -1/k • 1/u [du].

So, integrating will give you -1/k • ln(u).

Also, if you try differentiating your answer of -k • Ln(u) you will get -k/u and not 1/-ku.
4. Ahh, it was that simple. Thank you.

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