MATHEMATICS · Multi-part · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change
Problem
A function h is continuous on [0,4] and differentiable on (0,4). Its derivative h′ is known to be h′(t)=sin(t)+2. Two data tables are provided for antiderivatives of h′:
Table A (values of H)
t
0
1
2
3
4
H(t)
3
4.68
6.27
7.00
8.24
Table B (values of G)
t
0
1
2
3
4
G(t)
5
6.68
8.27
9.00
10.24
(a) Explain how the tabulated values support the claim that both H and G are antiderivatives of h′.
(b) Using only the information in the tables (no computation of definite integrals allowed), determine G(t)−H(t) for each listed value of t.
(c) State a conjecture about the exact value of G(t)−H(t) for all t in [0,4] and justify your reasoning based on the data.