Calculate the shaded finite region between the curve and the axis for the curve: 3x^2 +11x -4 = 0

3x²+11x-4=0 #Factorise to find where the curve crosses the x axis (3x-1)(x+4)=0 #Each bracket equals 0 x=1/3, -4  #Integrate the curve between these two points to find the area enclosed in the curve [x³ + 11/2 x² -4x] #With limits 1/3 to -4 ((1/3)³ + 11/2(1/3)²-4(1/3)) - ((-4)³ + 11/2(-4)² -4(-4)) = -40.6851851851... #The negitive sign only means the area is below the x axis Area is equal to 40.7 #Ussually round to 3d.p