Final answer:
To evaluate the integral ∫(4t³ - t² - 4) dt / (2√2), we integrate each term of the polynomial individually, sum them, and then divide by 2√2, including the constant of integration in the result.
Step-by-step explanation:
The student is asking to evaluate the integral of a function with respect to the variable t, and then to divide the result by 2√2. To solve this, we can integrate the function term by term. The integral of 4t³ is t⁴, the integral of -t² is -t³/3, and the integral of -4 is -4t. Summing these results and dividing by 2√2 gives us the final answer.
The integral ∫(4t³ - t² - 4) dt divided by 2√2 equals (t⁴/4 - t³/12 - 4t)/(2√2) + C, where C is the constant of integration.