definite integrals question

Question

The initial height and velocity of a mass attached to a spring is

h(0) = 10 cm

dh/dt = 9sin(0.45 t) cm/s

What is Δh on the interval [0,5]? (Be accurate to at least two decimal places.)

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What is h(5)?(Be accurate to at least two decimal places.)

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Answer 1

h(t) = ∫9sin(0.45t)dt = - 9/0.45cos(0.45t) + C = - 20cos(0.45t) + C; h(0) = - 20 + C = 10; C= 30

h(t) = 30 - 20cos(0.45t)

Δh = h(5) - h(0) = 30 - 20cos(2.25) - 10 = 32.56 cm