Let f be a differentiable function such that f(1)=π and f'(x)=√x^3+6. what is the value of f(5)?

By integrating f'(x) and knowing the value of f(1), we will get f(5) = 49.1

So we know that:

Integrating that, we get:

Where c is a constant of integration, to get its value, we need to use the condition:

f(1) = π

Then we have:

Then:

Now we just want to evaluate this in x = 5:

So the value of f(5) is 49.1

If you want to learn more, you can read:

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30 units^2

step-by-step explanation:

area is l × w

the length is 3

and the width is 10

3 × 10= 30 units squared

c. 1,233 miles