Find the exact value of .

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Find the exact value of

\displaystyle \int_{0}^{\pi} \frac{x}{\sqrt{1+x^{2}}}\,dx

. (a)

\sqrt{1+\pi^{2}}

(b)

\dfrac{1}{2}\bigl(\sqrt{1+\pi^{2}}-1\bigr)

(c)

\sqrt{1+\pi^{2}}-1

(d)

\ln\!\bigl(\pi+\sqrt{1+\pi^{2}}\bigr)