(calc 2000 * pi * (10 - ln 11))
(func f(x) pi / x ^ 2)
(simpson f .5 2)
(calc 3 * pi / 2)
(func f(x) pi * 2 * sqrt (1 + 1 / x ^ 4) / x)
(simpson f .5 2)
15.518133882370751
(func f(x) 3 * (x - 1) * (x  - 2) - 110 * x * (x - 2) + 91 * x * (x - 1))
(plot f 0 5)
(f 0)
(f 1)
(f 2)

;; 1.a
(func f(x) x * cos x)
(simpson f -1 1)

;; 1.b
(func f(x) exp x / (1 + exp x) ^ 2)
(simpson f -1 1)
(calc (exp 1 - 1) / (exp 1 + 1))

;; 3.a
(func f(x) ln x)
(simpson f (exp 1) (exp 2))
(calc (exp 2))

;; 3.b
(func f(x) x / (1 + x ^ 2) ^ 3)
(simpson f 0 1)
(calc 3 / 16)

;; 5.a diverges: integrate by substitution w = ln(x)

;; 5.b
(func f(x) 1 / sqrt (x + 5))
(mid f -5 10 1000)
(calc 2 * sqrt 15)