Question

Find the area bounded by the inverse of bijective function f(x)=4x³+6x, the x-axis and the ordinates x=0 and x=44

Answer 1

f(x) = 4x³ + 6x

∵ f(0) = 0 ⇒ f^-1(0) = 0

f(2) = 44 ⇒ f^-1(44) = 2

Bounded area

A = ₀∫² [44 - f(x)] dx

= ₀∫² [44 - 4x³ - 6x] dx

= (44x - x⁴ - 3x²)²₀

= 88 - 2⁴ - 3 x 2²

= 88 - 16 - 12

= 88 - 28

= 60.