For a continuous functionf,∫50f(x)dx= 10 and∫20190f(x)dx= 2020

Question

∫ 0 to 5, f(x)dx=10 ∫0 to 2019, f(x)dx=2020. Give the value of 2019 to 5 f(x)dx

Give the value o

Answer 1

As the integral from 0 to 2019 equals the integral from 0 to 5 + the integral from 5 to 2019, the integral from 5 to 2019 equals the integral from 0 to 2019 - the integral from 0 to 5, and the integral from 2019 to 5 equals minus( the integral from 0 to 2019 - the integral from 0 to 5) = the integral from 0 to 5 minus the integral from 0 to 2019 equals 10 - 2020 = -2010.