The definite integral J= _ 0 ^ 1 x ,dx is required when calculating certain series…

MATHEMATICS · Multi-part · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

The definite integral

J=\int_{0}^{1} \arctan x\,dx

is required when calculating certain series expansions. (a) Rewrite

J

so that only elementary functions appear inside the integral. (b) Determine the exact value of

J

. Present your work algebraically, including every intermediate step. (c) Compute a decimal approximation of

J

accurate to three decimal places.