How Calculate This integral in MATLAB?

[panda1234]

Hi,
How Calculate This integral in MATLAB?
in other word how to define this function?

 

[_Eduardo_]

- Solve by numerical methods \[x=y^3+e^y\] for \[x_0=0\] and \[x_1=10\]

\[x_0=0 \;\;\longrightarrow\;\; y_0=-0.7728829591\]
\[x_1=10 \;\;\longrightarrow\;\; y_1=1.672217398\]

Then if
\[x=y^3+e^y\;\;\longrightarrow\;\; dx=(3y^2+e^y)\;dy\]

\[\displaystyle\int_{0}^{10}{y(x)\;dx}=\displaystyle\int_{y_0}^{y_1}{y(3y^2+e^y)\;dy}= \left. (e^y(y - 1) + \frac{3}{4}y^4) \right |_{y_0}^{y_1} \]