The given quantities in theincreasing order from the smallest to the largest and explainthe reasoning.
A definite integral can be interpreted as a net area, that is, as difference of areas;
where, A1 is the region above x- axis and below the graph of f, and A2 is the region below x- axis and above the graph of f.
First, calculate the area for different intervals of a function.
To calculate the area, count the squares between the curve and the x- axis within the considered interval
A) For the interval [0, 8]∫08fxdx≈∫03fxdx+∫38fxdx=-3+10=7
B) For the interval [0, 3]∫03fxdx≈-3 since it lies below the x axis
C) For the interval [3, 8]∫38fxdx≈10
D) For the interval [4, 8]∫48fxdx≈9
E) And f'1≈-1 this is slope of the tangent line to function at x=1
Therefore, the increasing order is