Given that y= ((sin x)/(1 + cos x)) find (dy/dx) Evaluate ∫


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Question Number 33005 by Rio Mike last updated on 09/Apr/18

$G i v e n t h a t$ $y = \frac{s i n x}{1 + c o s x} f i n d \frac{d y}{d x}$ $E v a l u a t e$ $\int_{1}^{2} (x + 4) d x$
Commented by abdo imad last updated on 09/Apr/18

$\frac{d y}{d x} = \frac{c o s x (1 + c o s x) + {s i n}^{2} x}{{(1 + c o s x)}^{2}} = \frac{c o s x + {s i n}^{2} x + {c o s}^{2} x}{{(1 + c o s x)}^{2}} .$ $= \frac{1 + c o s x}{{(1 + c o s x)}^{2}} = \frac{1}{1 + c o s x} f o r x \in D_{y} .$ $★ \int_{1}^{2} (x + 4) d x = {[\frac{x^{2}}{2} + 4 x]}_{1}^{2} = 2 + 8 - \frac{1}{2} - 4$ $= \frac{3}{2} + 4 = \frac{11}{2} .$
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