f(x) + f(x + k) = n: find I1 + 2 I2 for integrals of f over given intervals
The same question, asked 2 times: 2021 Paper 5*, 28 Jun 2022. Every wording below, oldest first.
Try each one first, then open its answer.
Question 1
2021 Paper 5
89
Let f:R→R be a continuous function such that f(x)+f(x+1)=2, for all x∈R. If I1=∫08f(x)dx and I2=∫−13f(x)dx, then the value of I1+2I2 is equal to
Question 2
28 Jun 2022
158
Let f:R→R be continuous function satisfying f(x)+f(x+k)=n, for all x∈R where k>0 and n is a positive integer. If I1=∫04nkf(x)dx and I2=∫−k3kf(x)dx, then
