If t is measured in hours and f '(t) is measured in knots, then integral from 0 to 2 of f '(t)dt = ?
(Note: 1 knot = 1 nautical mile/hour)
To find the value of the integral, we need to perform antiderivation or integration of the given function f'(t) with respect to t, within the specified limits of integration.
Since f'(t) is measured in knots (nautical miles per hour) and t is measured in hours, we can interpret f'(t) as the rate of change of distance with respect to time.
Therefore, integrating f'(t) with respect to t will give us the total distance traveled by the object or the displacement over the given interval.
Using the Fundamental Theorem of Calculus, we can evaluate the integral as follows:
∫[0 to 2] f'(t)dt = F(2) - F(0)
where F(t) is the antiderivative or the integral of f'(t).
Since f'(t) represents the rate of change of distance, integrating it gives us the distance traveled. Thus, F(t) would represent the function that gives us the distance traveled at any specific time value.
Evaluating the integral, we need to find the antiderivative of f'(t). As f'(t) is given, let's assume f(t) is the original function.
Therefore, integrating f'(t) would give us:
∫[0 to 2] f'(t)dt = ∫[0 to 2] f(t)dt = F(2) - F(0)
Now, without knowing the specific function f(t), we can't provide an exact numerical value for the integral. However, we can still explain the process of evaluating the integral.
If you have the specific function f(t), you can find its antiderivative F(t) using various integration techniques like power rule, substitution, or integration by parts. After finding F(t), you can substitute the limits of integration (0 and 2) into F(t) to calculate F(2) and F(0). Then, subtracting F(0) from F(2) will give you the exact value of the integral.
But since we don't know the specific function f(t), we can't provide the direct numerical answer.