TMUA Yotta Paper 1 · Question 3

Community mocks

Yotta Paper 1 · Q3

Paper 1Calculus

Let $f_0(x)=x$ , and $f_{n+1}(x)=|f_n(x)-k|$ for non-negative integers $n$ , and positive real number $k$ . Let $\alpha$ and $\beta$ respectively equal the least and greatest values of $x$ for which $f_n(x)=0$ . Find the value of:

\int_\alpha^\beta f_n(x)\,\dd x

for $n>0$ , in terms of $n$ and $k$ .

nk^2

nk^2-k^2

kn^2

nk

k(n-1)^2

nk^2-1

Read the questions freely. Sign in to check your answer, see the worked solution and save your progress.