Define g(x)= cases x^ 2 , & 0 x<2, 4-x, & x 2

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

Problem

Define g(x)={x2,0≤x<2,4−x,x≥2,g(x)=\begin{cases}x^{2}, & 0\le x<2,\\ 4-x, & x\ge 2,\end{cases} and let R(x)=∫1g(x)1+t6 dt.R(x)=\int_{1}^{g(x)} \sqrt{1+t^{6}}\,dt. Determine R′(3)R'(3).

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