Let . What is…

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

Problem

Let R(x)=∫−1sin⁡(x2)et3 dtR(x)=\displaystyle\int_{-1}^{\sin(x^{2})} e^{t^{3}}\,dt. What is R′(x)R'(x)? (a) 2x esin⁡3(x2)2x\,e^{\sin^{3}(x^{2})} (b) 6xcos⁡(x2)sin⁡2(x2) esin⁡3(x2)6x\cos(x^{2})\sin^{2}(x^{2})\,e^{\sin^{3}(x^{2})} (c) 2xcos⁡(x2) esin⁡3(x2)2x\cos(x^{2})\,e^{\sin^{3}(x^{2})} (d) 2xcos⁡(x2) ex62x\cos(x^{2})\,e^{x^{6}}

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