Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = 2t + sin(t) and v(0) = 4.

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a(t) = dv/dt so v(t) = int(2t+sint)

replace a(t) with dv/dt
and write
a= 2t+sin t as
dv/dt = 2t + sin t
dv = (2t +sin t ) dt

now integrate both sides

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