Given our function f(x) = x^3 + 2x^2 - 5x - 6 the shaded region required is the sum of two areas which we will call A (shaded region above the x axis) and B (shaded region below the x axis).

To find A we need to integrate f(x) with respect to x between two limits i.e. from the lowest value of x for region A, to the greatest value of x for region A.

To find these limits we must calculate the values of x at which f(x) cuts across the x axis, and as you know, these are the roots of our cubic equation.

There are a number of ways to find the roots of our equation - the easiest approach in this case seems to be by factorising the cubic.

To factorise f(x) we can use the polynomial factor theorem which tells us that:

if f(a) = 0 then (x-a) is a factor of f(x).

From your graph you might consider the value: a = -1

f(-1) = (-1)^3 + 2(-1)^2 -5(-1) - 6
= 0

This satisfies the condition of the factor theorem so:
=> (x - (-1)) is a factor of f(x).

We can use this to factorise f(x) completely and so find all the roots:

... prism, then we just subtract the two to find the volume ... be two separate components or parts of the graph left over. ... 4. The area of a trapezoid is half of the ...

... is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the ...

... c) Determine (state yes or no) whether the graph in part (a) has an ... square feet room 2: A = (12)(15) = 180 square feet total area: A = 108 ... Now, find the price: ...

... up the integral ranges to find a particular probability area. ... 3/4 , Y_2 >= 1/2) b) Find P(Y_1 ... From your graph, determine whether the region of integration is ...

...Find the area of the shaded region shown below ... use the change of variable technique to find an antiderivative in ... sketch the graph of each function and find the ...

... c. find the feasible point that is closest to the ... Use this graph to answer the questions. ... The shaded area satisfies feasibility of each of the constraints and ...

... The graph and table below From the above information it is found show ... round your 3.14*56.25 = 176.625 answer to one decimal Area of the ...Find m∠a and m∠b. 38 ...

... Then find the area where the three inequalities are all satisfied. ... Therefore, the feasible region is the shaded area in the following graph. y 18.5. 10. ...