Question

Use the Trapezoidal Rule to approximate ∫2−1ex2dx using n=4. Round your answer to the nearest hundredth.

Answer 1

`\begin{gathered} \int_{\text{ -}1}^2e^(x^2)=(h)/(2)(e^{(\text{ -1\rparen}^2}+e^(2^2)) \\ \\ h=(b\text{ - }a)/n=(2\text{ - \lparen-1\rparen\rparen/4=}(3)/(8)\text{ } \\ \int_{\text{ -1}}^2e^(x^2)=(3)/(8)(e+2e^{(1)/(16)}+2e^{(1)/(4)}+2e^{(25)/(16)}+e^4) \\ \\ =(3)/(8)(2.72+2.13+2.57+9.54+54.6) \\ \\ =(3)/(8)(71.56)=26.84 \end{gathered}`