differentiation question 2

**peteryellow** · August 30th 2009, 12:31 PM

derivate $\int_{sin(x)}^{0} \frac{dt}{\sqrt{1-t^2}}$ ,

$|x|< \frac{\pi}{2}$

**skeeter** · August 30th 2009, 01:22 PM

Originally Posted by peteryellow

derivate $\int_{sin(x)}^{0} \frac{dt}{\sqrt{1-t^2}}$ ,

$|x|< \frac{\pi}{2}$

$\int_{sin(x)}^{0} \frac{dt}{\sqrt{1-t^2}} = -\int_0^{sin(x)} \frac{dt}{\sqrt{1-t^2}}$

$\frac{d}{dx}\left[-\int_0^{sin(x)} \frac{dt}{\sqrt{1-t^2}} \right]= -\frac{1}{1-\sin^2{x}} \cdot \cos{x} = -\sec{x}$

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