QuestionUse the Fundamental Theorem to evaluate the definite integral exactly. $$\int_{0}^{3}\left(12 x^{2}+1\right) d x$$
Enter the exact answer. $$\int_{0}^{3}\left(12 x^{2}+1\right) d x=$$ $\square$ eTextbook and Media

Studdy Solution
Subtract the value of the antiderivative at the lower limit from the value at the upper limit:
$$\int_{0}^{3}(12x^2 + 1) \, dx = F(3) - F(0)$$ $$\int_{0}^{3}(12x^2 + 1) \, dx = 111 - 0$$ $$\int_{0}^{3}(12x^2 + 1) \, dx = 111$$
The exact value of the definite integral is:
$$\boxed{111}$$