#### To determine

**To list:**

The given quantities in theincreasing order from the smallest to the largest and explainthe reasoning.

#### Answer

B<E<A<D<C

#### Explanation

**1) Concept:**

A definite integral can be interpreted as a net area, that is, as difference of areas;

∫abf(x)dx=A1-A2

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.

**2) Given:**

**Graph:**

**3) Calculation:**

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

B<E<A<D<C

**Conclusion:**

Therefore,

B<E<A<D<C