- #1

- 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.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

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

- #1

- 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

- 35,638

- 7,513

[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

- 35,638

- 7,513

Then

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

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

Share: