Jun 10, 2015 #1 P panda1234 Full Member level 2 Joined Jan 22, 2015 Messages 125 Helped 4 Reputation 8 Reaction score 4 Trophy points 18 Activity points 1,172 Hi, How Calculate This integral in MATLAB? in other word how to define this function?
Jun 13, 2015 #2 _Eduardo_ Full Member level 5 Joined Aug 31, 2009 Messages 295 Helped 118 Reputation 238 Reaction score 103 Trophy points 1,323 Location Argentina Activity points 2,909 - 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 \[x=y^3+e^y\;\;\longrightarrow\;\; dx=(3y^2+e^y)\;dy\] \[\displaystyle\int_{0}^{10}{y(x)\;dx}=\displaystyle\int_{y_0}^{y_1}{y(3y^2+e^y)\;dy}= \left. (e^y(y - 1) + \frac{3}{4}y^4) \right |_{y_0}^{y_1} \]
- 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 \[x=y^3+e^y\;\;\longrightarrow\;\; dx=(3y^2+e^y)\;dy\] \[\displaystyle\int_{0}^{10}{y(x)\;dx}=\displaystyle\int_{y_0}^{y_1}{y(3y^2+e^y)\;dy}= \left. (e^y(y - 1) + \frac{3}{4}y^4) \right |_{y_0}^{y_1} \]