Final answer:
The student needs to evaluate the integral of 4x^2 - 3 from 1 to 2 using a specific entry from a table of integrals. Using general integral rules, the integral of a polynomial is found by applying the power rule to each term and summing the results.
Step-by-step explanation:
The question asks us to evaluate the integral of 4x^2 - 3 from 1 to 2 using the indicated entry in the table of integrals, which corresponds to entry number 39. To solve this, we refer to entry 39 which presumably has the general form of the integral needed to integrate 4x^2 - 3. Without the specific form of entry 39, we can assume it involves integrating a polynomial. A typical approach to integrating a polynomial like this would be to integrate each term separately, summing the results.
For example, the integral of 4x^2 from 1 to 2 would be evaluated using the power rule, resulting in \( \frac{4}{3}x^3 \) evaluated from 1 to 2. Similarly, the integral of -3 over the same interval would simply be -3x, also evaluated from 1 to 2. We then combine the results from both integrations to get the answer.