Application Of Integration

\(\text { Match the following : }\)

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(i)	\( \int_0^{\pi / 2}(\sin x)^{\cos x}\left(\cos x \cot x-\log \left(\sin ^x\right)^{\sin } x\right) \mathrm{d} x \)	(A)	1
(ii)	\( \text { Area bounded by }-4 y^2=x \text { and } x-1=-5 y^2 \)	(B)	0
(iii)	Cosine of the angle of intersection of $y=3^{x-1} \log x$ and $y=x^{x-1}$ is	(C)	6 In 2
(iv)	\( \frac{d y}{d x}=\frac{2}{(x+y)} ; y\left(-\frac{2}{3}\right)=0 \text {, then value of constant }(\mathrm{k})= \)	(D)	4/3