Calculate the following integral, assuming that ∫10𝑓(𝑥)𝑑𝑥 ∫ 0 1 f ( x ) d x = -10,

Question

Calculate the following integral, assuming that ∫1(up) 0(down) 𝑓(𝑥) dx = -10,  ∫2(up)0(down)𝑓(𝑥)𝑑𝑥 = -10,  ∫4(up)1(down)𝑓(𝑥)dx =-10

∫1(up) 2(down) 𝑓(𝑥)𝑑𝑥 =

Answer 1

∫_{(from 0 to 1)}f(x)dx = -10 and ∫_{(from 0 to 2)}f(x)dx = -10

So, ∫_{(from 1 to 2)}f(x)dx = ∫_{(from 1 to 0)}f(x)dx + ∫_{(from 0 to 2)}f(x)dx

= -∫_{(from 0 to 1)}f(x)dx + (-10) = -(-10) - 10 = 0