Question

To sketch the rough graph of \(g\).

Short answer

The graph for function \(f\) is shown in Figure 1 .

Step-by-step solution

Given data

The integral function is \(g(x) = \int_0^x f (t)dt\).

Concept used of Integral Calculus

We define integrals as the function of the area bounded by the curve\(y = f(x)\),\(a \le x \le b\), the\(x\)-axis, and the ordinates\(x = a\) and\(x = b\), where\(b > a\).

Let\(x\)be a given point in (\(a\),\(b\)). Then\(\int_a^b f (x)dx\)represents the area function.

This concept of area function leads to the fundamental theorems of integral calculus.

Plot the Graph

Plot the graph for function \(f\) by the use of the calculated values of \(0,\frac{1}{2},0, - \frac{1}{2},0,1.5,4\), and for the functions \(g(0)\), \(g(1),g(2),g(3),g(4),g(5),g(6)\), and \(g(7)\) respectively.

Draw the graph for the function of \(f\) as in Figure (1).