Let and be the real numbers such that _ x 0 1 x^3 ( 2 _0^x 1 1-t^2 ,dt + x x ) = 2

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

\alpha

and

\beta

be the real numbers such that

\lim_{x \rightarrow 0} \frac{1}{x^3} \left( \frac{\alpha}{2} \int_0^x \frac{1}{1-t^2}\,dt + \beta x \cos x \right) = 2.

Then the value of

\alpha + \beta

is ____.