\begin{tikzpicture}[scale=0.7]

\draw[->] (9,-1.5)--(11,-1.5) node[below] {$x$};

\draw[dashed] (9,-1.5)--(8,-1.5); \draw[dashed] (5,-1.5)--(4,-1.5); \draw[dashed] (1,-1.5)--(0,-1.5);

\draw (-1,-1.5)--(0,-1.5); \draw (8,-1.5)--(5,-1.5);\draw (4,-1.5)--(1,-1.5);

\draw[smooth,samples=100,domain=1:4] plot(\x,{sin(\x/2 r)+2});

\draw[dashed,smooth,samples=100,domain=4:5] plot(\x,{sin(\x/2 r)+2});

\draw[smooth,samples=100,domain=5:8] plot(\x,{sin(\x/2 r)+2});

\draw[dashed,smooth,samples=100,domain=8:9] plot(\x,{sin(\x/2 r)+2});

\draw[smooth,samples=100,domain=5:8] plot(\x,{(\x-1)*(\x-9)/16});

\draw[dashed,smooth,samples=100,domain=4:5] plot(\x,{(\x-1)*(\x-9)/16});

\draw[smooth,samples=100,domain=1:4] plot(\x,{(\x-1)*(\x-9)/16});

\draw[dashed,smooth,samples=100,domain=8:9] plot(\x,{(\x-1)*(\x-9)/16});

\draw (2.5,3)--(2.5,4)--(0,3)--(0,-3)--(2.5,-2)--(2.5,-0.6); \draw[dashed] (2.5,3)--(2.5,-0.6);

\draw (6.5,1.9)--(6.5,4)--(4,3)--(4,-3)--(6.5,-2)--(6.5,-0.8); \draw[dashed] (6.5,1.9)--(6.5,-0.7);

\draw (10.5,4)--(8,3)--(8,-3)--(10.5,-2)--(10.5,4);

\draw [thick] (1,2.5) to[out=190,in=160] (1,0);

\draw [dashed,thick] (1,2.5) to[out=-20,in=0] (1,0);

\draw [thick] (5,2.6) to[out=200,in=150] (5,-1);

\draw [dashed,thick] (5,2.6) to[out=-20,in=0] (5,-1);

\draw [thick,] (9,1) to[out=190,in=160] (9,0);

\draw [thick] (9,1) to[out=-20,in=0] (9,0);

\draw[dashed] (1,0)--(1,-1.5) node[below] {$a$};

\draw[dashed] (9,0)--(9,-1.5) node[below] {$b$};

\draw[dashed] (5,-1)--(5,-1.5) node[below] {$x$};

\draw[fill=black,pattern=north east lines,pattern color=black] (5,2.6) to[out=200,in=150] (5,-1)

to[out=0,in=-20] (5,2.6)--cycle;

\end{tikzpicture}