The limit _ n _ i=1 ^ n ( (1+ b i n ) ) b n equals Determine the value of .

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

Problem

The limit

\lim_{n\to\infty}\sum_{i=1}^{n}\bigl(\sin\bigl(1+\tfrac{b i}{n}\bigr)\bigr)\cdot\tfrac{b}{n}

equals

\displaystyle \int_{1}^{4}\sin x\,dx.

Determine the value of

b