91Ó°ÊÓ

Find, to two decimal places, the \(x\) -coordinate of the centroid of the region in the first quadrant bounded by the \(x\) -axis, the curve \(y=\tan ^{-1} x,\) and the line \(x=\sqrt{3}\).

Find the centroid of the region bounded by the graphs of \(y=x+\cos x\) and \(y=0\) for \(0 \leq x \leq 2 \pi\).

Show that if \(f(x)\) is integrable on every interval of real numbers and \(a\) and \(b\) are real numbers with \(a