Question

By Simpson’s \(1/3\)rd rule, the approximate value of the integral \(\int_1^2 e^{-x/2}dx\) using four intervals, is

• A. 0.377
• B. 0.487
• C. 0.477
• D. 0.387

Hint:

For Simpson’s rule: coefficients follow pattern \(1,4,2,4,1\).

Answer 1

The Correct Option is C

Concept: Simpson’s rule: \[ \int_a^b f(x)dx \approx \frac{h}{3}[f_0 + 4f_1 + 2f_2 + 4f_3 + f_4] \] \[ h=\frac{2-1}{4}=0.25 \] Compute values: \[ f(x)=e^{-x/2} \] Substitute values and simplify: \[ \approx 0.477 \]