Question concerning integral equations

**Tau** · December 10th 2008, 04:31 AM

Hi

Something I don't understand about the derivation of integrals is wether the result will be
y(x) or -y(x)

(Given that we start with $\int_{a}^{b}y(t)\delta t$ )

Explanation much appreciated.

Thanks for your replies.

**mr fantastic** · December 10th 2008, 04:43 AM

Originally Posted by Tau

Hi

Something I don't understand about the derivation of integrals is wether the result will be
y(x) or -y(x)

(Given that we start with $\int_{a}^{b}y(t)\delta t$ ) Mr F says: If a and b are constants then the derivative of this expression is zero since the integral is a number.

Explanation much appreciated.

Thanks for your replies.

$\frac{d}{dx} \left[ \int_{a}^x y(t) \, dt \right] = y(x)$ .

$\frac{d}{dx} \left[ \int_{x}^a y(t) \, dt \right] = \frac{d}{dx} \left[ -\int_{a}^x y(t) \, dt \right] = - y(x)$ .

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