Use the Trapezoidal Rule to approximate the value of the definite integral , Round your answer to three decimal places.
A) 4.662
B) 6.764
C) 4.655
D) 2.793
E) 2.796

Question

Use the Trapezoidal Rule to approximate the value of the definite integral  ,  Round your answer to three decimal places. ​
A) 4.662 
B) 6.764 
C) 4.655 
D) 2.793 
E) 2.796

Quizplus · Accepted Answer

Applying the Trapezoidal Rule with $n=5$, we have:

\begin{align*}
\int_{1}^{2} e^{-x^2} \, dx &\approx \frac{1}{2\cdot 5}\left(e^{-1^2}+2e^{-\left(\frac{3}{5}ight)^2}+2e^{-\left(\frac{5}{5}ight)^2}+2e^{-\left(\frac{7}{5}ight)^2}+e^{-2^2}ight) \
&\approx 4.655
\end{align*}

Therefore, the best choice is $\boxed{	extbf{(C)}}$.

Use the Trapezoidal Rule to Approximate the Value of the Definite