Question

Suppose that (f(x) = int t⁴ , dt) where (1 leq t leq x). Find (f(3)).

Answer 1

To find f(3), the definite integral of t^4 from 1 to 3 is calculated, yielding a result of 48.4.

Step-by-step explanation:

To find f(3), you need to evaluate the definite integral of the function t4 from t = 1 to t = 3. The integral of t4 with respect to t is (1/5)t5 plus a constant of integration. Since this is a definite integral, the constant of integration is not needed, and we evaluate the integral at the upper and lower limits and subtract.

Following the integral calculus, we have:

1. Integrate t4 to get (1/5)t5.
2. Evaluate the integral from 1 to 3: (1/5)×35 - (1/5)×15.
3. Calculate the result: (1/5)×243 - (1/5)×1 = 48.6 - 0.2 = 48.4.

Therefore, f(3) is 48.4.