- #1

e^(i Pi)+1=0

- 247

- 1

This is something I can churn through mechanically but I never "got." Any links / explanations that can help build my intuition about this would be helpful.

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- Thread starter e^(i Pi)+1=0
- Start date

- #1

e^(i Pi)+1=0

- 247

- 1

This is something I can churn through mechanically but I never "got." Any links / explanations that can help build my intuition about this would be helpful.

- #2

Mark44

Mentor

- 36,709

- 8,708

[itex]\frac{d}{dx} \int_a^b f(x)=f(b)[/itex]

This is something I can churn through mechanically but I never "got." Any links / explanations that can help build my intuition about this would be helpful.

What you have is incorrect, assuming that both a and b are constants.

[tex]\frac{d}{dx} \int_a^b f(x) dx =0[/tex]

The way this is usually presented is like so:

[tex]\frac{d}{dx} \int_a^x f(t) dt =f(x)[/tex]

- #3

Mark44

Mentor

- 36,709

- 8,708

Then

$$ \int_a^x f(t) dt = F(x) - F(a)$$

So $$ d/dx \int_a^x f(t) dt = d/dx( F(x) - F(a)) = F'(x) - 0 = f(x)$$

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