Chapter 15.3, Problem 1CFU

To determine

Find the equation of a function for the given series to find the area under the graph.

Answer to Problem 1CFU

The equation of a function is $y=x^4$ .

Explanation of Solution

Given:

The given seriesis $1^4+2^4+3^4+---+n^4$ .

Calculation:

Width of the each bin $=$ $1$

Height of the each bin $=$ $x^4$

Area of the each bin $=1\cdot x^4$

Where $x=1,2,3---,n$ .

Total area

  $\begin{array}{l}=1\cdot 1^4+1\cdot 2^4+1\cdot 3^4+---++1\cdot n^4\\ =1^4+2^4+3^4+---+n^4\end{array}$

Hence an equation of the function is $y=x^4$ .