Find the area enclosed between
f(x)=0.4x^2+5
and
g(x)=x
From x=-5 to x=8
Area= INT (f(x)-g(x))dx frm -5 to 8
= INT (.4x^2+5-x)dx
= .4/3 x^3 + 5x-x^2/2 on limits
check my thinking.
To find the area enclosed between two curves, you need to calculate the definite integral of their difference over the given interval. In this case, we have two curves: f(x) = 0.4x^2 + 5 and g(x) = x.
Step 1: Determine the points of intersection
To find the area between the curves, we need to determine the x-values where the two curves intersect. Set f(x) equal to g(x) and solve for x:
0.4x^2 + 5 = x
Step 2: Solve for x
0.4x^2 - x + 5 = 0
This is a quadratic equation, so we can use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / 2a
Applying the quadratic formula, we have:
x = (-(-1) ± √((-1)^2 - 4*0.4*5)) / (2*0.4)
x = (1 ± √(1 - 8)) / 0.8
x = (1 ± √(-7)) / 0.8
Since the discriminant is negative, there are no real solutions. Therefore, the curves do not intersect on the given interval. This means that there is no enclosed area between the two curves from x = -5 to x = 8.