Let C(x)= _ x ^ 3 (t^ 2 -4 ) ,dt+ _ 1 ^ x^ 2 (t^ 2 -4 ) ,dt

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

Problem

Let C(x)=∫x3(t2−4) dt+∫1x2(t2−4) dt,x>0.C(x)=\int_{x}^{3} \bigl(t^{2}-4\bigr)\,dt+\int_{1}^{x^{2}} \bigl(t^{2}-4\bigr)\,dt, \qquad x>0. Which of the following is equal to C′(x)C'(x)? (a) 2x5+x2−8x−42x^{5}+x^{2}-8x-4 (b) −2x5+x2+8x−4-2x^{5}+x^{2}+8x-4 (c) 2x5−x2−8x+42x^{5}-x^{2}-8x+4 (d) 2x5−x2+8x−42x^{5}-x^{2}+8x-4

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