Question

Given that the value of the integral \[ \int_1^9 (x^2 - 2)\, dx \] calculated using the Simpson's 1/3 rule with four uniform subintervals over the interval [1,9] is given by \[ f(1) + \alpha^2 + \frac{8}{3}, \] then the possible value of \( \alpha \) is _______
 

• A. $\alpha = 15$
• B. $\alpha = 14$
• C. $\alpha = 13$
• D. $\alpha = 12$

Hint:

Use Simpson's 1/3 rule for numerical integration to estimate integrals. Choose an even number of intervals for better accuracy.

Answer 1

The Correct Option is A

Use Simpson's rule for numerical integration. The formula for Simpson's 1/3 rule is: \[ I = \frac{h}{3} \left( f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + f(x_4) \right) \] By applying this formula and solving for $\alpha$, we get $\alpha = 15$.