drawing arrows on curves and shading regions in TikZ

I need to draw the following figure in my latex using TikZ. I did the following:

\begin{tikzpicture}
\draw (-2,0) -- (2,0);
\draw (0,-2) -- (0,2);
\draw (0,0) circle (1cm);
\draw (1,-.3) node[right] {(2,0)};
\draw (-1,-.3) node[left] {(-2,0)};

\end{tikzpicture}


But how can I shade the upper semi-circle and how can I draw the arrows in between? Additional Question Thank you so much for your answer. But I have one more doubt: If I use these command in my question I get the diagram right aligned and above the question. But I need it to be beside the question. And sometimes I need to define exactly where I want it to be. What should I do for this?

\question Evaluate $\displaystyle\iint_R dxdy,$ where $R$ is the shaded region in the figure.
\begin{tikzpicture}
\draw (-2,0) -- (2,0);
\draw (0,-2) -- (0,2);
\draw (0,0) circle (1cm);
\draw (1,-.3) node[right] {(2,0)};
\draw (-1,-.3) node[left] {(-2,0)};
\draw[pattern=north west lines] (-1,0) --(1,0) arc[start angle=0, end angle=180, radius=1cm];
\end{tikzpicture} • Some body give me the solution for the second question. – David Oct 12 '14 at 14:55
• Andd suppose i have two different curves and i need to shade the area between the curve how can i do.. – David Oct 12 '14 at 14:56
• We appreciate one question per post. If you have another question please post a new one. However, for your first question see my previous comment under my answer. As for second question, what are the two curves? Please add some (full) code. – user11232 Oct 12 '14 at 15:01
• $y=x^2$ and $x=y^2$@HarishKumar – David Oct 12 '14 at 15:16

Perhaps there is a better way, but here is one brute force way. You need to load the tikzlibraries patterns and arrows.meta in your preamble.

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{patterns, arrows.meta}
\begin{document}
\begin{tikzpicture}
\draw (-2,0) -- (2,0);
\draw (0,-2) -- (0,2);
\draw (0,0) circle (1cm);
\draw (1,-.3) node[right] {(2,0)};
\draw (-1,-.3) node[left] {(-2,0)};
\draw[pattern=north west lines] (0,-1) --(0,1) arc[start angle=90, end angle=-90, radius=1cm];
\draw[-{To[length=5pt,width=10pt]}] (0,-1) arc[start angle=-90, end angle=-45, radius=1cm];
\draw[-{To[length=5pt,width=10pt]}] (0,1)  arc[start angle=90, end angle=135, radius=1cm];

\end{tikzpicture}
\end{document} • Kindly revisit my question. I Have onemore doubt. Thank you for ur help...@darthbith – David Oct 12 '14 at 14:42
• If i use these command it is giving this error. {I can't find file 'tikzlibraryarrows.meta.code.tex} give me a solution please. @darthbith – David Oct 12 '14 at 14:48
• @David Two things: 1. If you have a new question, please ask a new question instead of asking your new question within this question. 2. You should use the line \usetikzlibrary{arrows.meta}. It seems like you are trying to use \usetikzlibrary{tikzlibraryarrows.meta} which is incorrect – darthbith Oct 12 '14 at 14:59
• sure...@darthbith – David Oct 12 '14 at 15:01

This uses decorations and \clip.

\documentclass[tikz]{standalone}
\usetikzlibrary{patterns,decorations.markings}
\begin{document}
\begin{tikzpicture}[arrowmark/.style 2 args={decoration={markings,mark=at position #1 with \arrow{#2}}}]
\draw (-2,0) -- (2,0);
\draw (0,-2) -- (0,2);
\begin{scope}
\clip (0,-1) rectangle (1,1);
\draw[draw=none,pattern=north west lines,pattern color=black!50](0,0)
circle(1cm);
\end{scope}
\draw[postaction={decorate},arrowmark={.375}{>},arrowmark={.875}{>}
]  (0,0) circle (1cm);
\draw (1,-.3) node[right] {(2,0)};
\draw (-1,-.3) node[left] {(-2,0)};
\end{tikzpicture}
\end{document} • Kindly revisit my question. I Have onemore doubt. Thank you for ur help...@Harish – David Oct 12 '14 at 14:43
• @David Add baseline={(current bounding box.center)} to tikzpicture options like \begin{tikzpicture}[baseline={(current bounding box.center)}...] – user11232 Oct 12 '14 at 14:57

Just 4 fun with PSTricks.

\documentclass[pstricks,border=12pt,12pt]{standalone}
\begin{document}
\begin{pspicture}(-5,-5)(5,5)
\pswedge[fillstyle=vlines,hatchcolor=gray]{3}{-90}{90}
\psline(0,-5)(0,5)
\psline(-5,0)(5,0)
\psset{arrows=->,arrowscale=2}
\psarc(0,0){3}{-46}{135}
\psarc(0,0){3}{134}{-45}
\uput[-90](4,0){$(2,0)$}
\uput[-90](-4,0){$(-2,0)$}
\end{pspicture}
\end{document} 