using Plots
using Roots
using SymPy
using QuadGK

f(x) = exp(-x)
g(x) = x^2
h(x) = f(x) - g(x)
ip = find_zero(h, 1)
plot(f, 0, ip)
plot!(g)

quadgk(h, 0, ip)

h(x) = f(x) - g(x) > 0 ? f(x) - g(x) : 0.0
quadgk(h, 0, 1)

r(x) = 1 + x/10
v(x) = pi * r(x)^2
quadgk(v, 0, 5)

r(x) = 1 + x/10
c(x) = (2r(x))^2		# area of square is d * d with d= 2r
quadgk(c, 0, 5)





7850 * 2.2 * (1/39.3)^3



f(x) = x^2
a,b = -2, 1
mid = (a + b)/2
secant(f, a, b) = x->f(a) + (f(b)-f(a))/(b-a)*(x-a)
topline = secant(f,a,b)
h(x) = topline(x) - f(x)
a, err = quadgk(h, a, b)



@vars x y
solve(1-y-sqrt(x^2+y^2), y)









f(x) = x < 500 ? 126.0 + (40-126)/(500-0)*x : 40.0 + (0 - 40)/(55-0)*(x-500)





f(x) = x^4 - 2.3x^3 + 4
g(x) = 4
plot(f, 0, 2.5)
plot!(g)