$\text { Use the Trapezoid Rule to approximate the value of the definite integral } \int _ { 0 } ^ { 2 } x ^ { 4 } d x \text { wth }$ $n = 4$.
Round your answer to four decimal places.
A) $7.0625$
B) $5.7813$
C) $7.0313$
D) $6.5625$
E) $28.2500$

Question

$\text { Use the Trapezoid Rule to approximate the value of the definite integral } \int _ { 0 } ^ { 2 } x ^ { 4 } d x \text { wth }$ $n = 4$. 
Round your answer to four decimal places.
A) $7.0625$
B) $5.7813$
C) $7.0313$
D) $6.5625$
E) $28.2500$

Quizplus · Accepted Answer

The Trapezoid Rule with n = 4 is:$$\frac{b-a}{2n}[f(x_0)+2f(x_1)+2f(x_2)+2f(x_3)+f(x_4)]$$where $a=0, b=2, n=4$, and $f(x)=x^4$.So,$$\frac{2-0}{2(4)}[f(0)+2f(0.5)+2f(1)+2f(1.5)+f(2)]$$$$=\frac{1}{8}[0+2(0.0625)+2(0.5)+2(1.0625)+4]$$$$=\frac{1}{8}[7.0625]=0.8828$$