For a continuous function f(x), f(1) = 11, and integral 1 to 5 f'(x)dx = 9. Determine f(5).
Help is greatly appreciated!
well, you know that
∫[1,5] f'(x) dx = f(5) - f(1)
So plug in your numbers.
To determine f(5), we can use the Fundamental Theorem of Calculus, which states that the definite integral of a function's derivative over an interval will yield the difference in the values of the original function at the interval's endpoints. In this case, we are given the integral from 1 to 5 of f'(x)dx, which equals 9. This implies that the difference between f(5) and f(1) is 9.
To find f(5), we need to find f(1). We know that f(1) = 11 according to the given information. Therefore, we can write the equation:
f(5) - f(1) = 9
Now, we can substitute f(1) = 11 into the equation:
f(5) - 11 = 9
To isolate f(5), we can add 11 to both sides of the equation:
f(5) = 9 + 11
Simplifying:
f(5) = 20
Therefore, f(5) = 20.