Apentix/AP Calculus AB/Unit 8: Applications of Integration/Question

AP Calculus ABmediummcq1 pt

A particle moves along a line with velocity $v(t)=6t^2+2$ . If its position satisfies $s(1)=5$ , what is $s(3)$ ?

A.

61

B.

56

C.

65

D.

60

Explanation

Core Concept

By the Fundamental Theorem, $s(3)=s(1)+\int_1^3(6t^2+2)\,dt=5+[2t^3+2t]_1^3=5+56=61$ .

Correct Answer

A $61$

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