Use Simpson's Rule to approximate the integral with answers rounded to four decimal places.
A)3.0265
B)2.2028
C)2.4774
D)2.7519

Question

Use Simpson's Rule to approximate the integral with answers rounded to four decimal places. 
A)3.0265 
B)2.2028 
C)2.4774 
D)2.7519

Quizplus · Accepted Answer

Simpson's Rule is used to approximate the integral of a function using quadratic polynomials. It is given by the formula: 
∫a^b f(x)dx ≈ (b-a)/6 [f(a) + 4f((a+b)/2) + f(b)]
Using this formula with a=0, b=2 and f(x)=x^2+1, we get:
∫0^2 (x^2+1)dx ≈ (2-0)/6 [f(0) + 4f(1) + f(2)]
≈ (1/3)[1 + 4(2^2+1) + 2^2+1]
≈ 2.4774, rounded to four decimal places.
Therefore, the best choice is C.

Use Simpson's Rule to Approximate the Integral with Answers Rounded