Let f(x)= cases x^ 2 ,&-1 x 1

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

f(x)=\begin{cases}x^{2},&-1\le x\le 1,\\c x,&1< x\le 3.\end{cases}

\lim_{n\to\infty}\sum_{i=1}^{n}f\!\left(-1+\tfrac{4i}{n}\right)\cdot\tfrac{4}{n}=14,

find the value of the constant

c