Question

If f(x) = 3x22, evaluate afI: ()k=1

Answer 1

Step 1: Write out the function given

$f(x)=3x^2-x$

Step 2: Interprete the question given

$\sum ^5_{k\mathop=1}f(\frac{k}{2})$

The question requested we find the summation of the first five terms for f(k/2), when k is 1, 2, 3, 4, and 5

Step 3: Find the expression for f(k/2)

$\begin{gathered} f(\frac{k}{2})=3(\frac{k}{2})^2-\frac{k}{2} \\ =\frac{3k^2}{4}-\frac{k}{2} \\ =\frac{3k^2-2k}{4} \end{gathered}$$\begin{gathered} =\frac{3(1)^2-2(1)}{4}+\frac{3(2)^2-2(2)}{4}+\frac{3(3)^2-2(3)}{4}+\frac{3(4)^2-2(4)}{4}+\frac{3(5)^2-2(5)}{4} \\ =\frac{1+8+21+40+65}{4} \\ =\frac{135}{4} \\ =33.75 \end{gathered}$

Hence, the answer is 33.75