Find the total area bounded by The given function in the xax

(14 pts) 1. Find the total area bounded by the given function and the x-axis Sketch a graph of the given function and label the important points. Shade the appropriate areas being calculated and place a plus or a minus sign in the shaded area to represent whether the area is classified as positive or negative. Set up the sequence of integrals, using addition and subtraction, that must be used to calculate the total area. USE YOUR CALCULATOR to calculate the sequence of integrals g(x)=x4 + x3-13x2-x+ 12

Solution

solving for the roots

we get by factorization as :-4,-1,1,3

hence now inegrate within this interval: integral of (x4+x313x2x+12) from -4 to -1 = -88.650 (negative since below x axis)

and (x4+x313x2x+12) from 1 to 3 = -24.267 (

negative since below x axis)

)

adding we get :

adding two we get = -112.917