A company determined that the marginal cost, \( C^{\prime}(x) \) of producing the \( x \) th unit of a product is given by \( C^{\prime}(x)=x^{3}-6 x \). Find the total cost function \( C \), assuming that \( C(x) \) is in dollars and that fixed costs are \( \$ 6000 \).

Suppose \( \int_{2}^{4} f(x) d x=6, \int_{2}^{7} f(x) d x=-2 \), and \( \int_{2}^{7} g(x) d x=4 \). Evaluate the following integrals. \( \int_{7}^{2} g(x) d x=-4 \) (Simplify your answer.) \( \int_{7}^{7} 5 g(x) d x=20 \) 2 (Simplify your answer.) \( \int_{2}^{7}[g(x)-f(x)] d x=\square \) 2 (Simplify your answer.)

\( \int_{2}^{7} 5 g(x) d x=\square \) (Simplify your answer.)

Evaluate the integral. \( \int_{1}^{4}\left(x^{2}-1\right) d x=\square \) (Simplify your answer.)

Suppose \( \int_{2}^{4} f(x) d x=6, \int_{2}^{7} f(x) d x=-2 \), and \( \int_{2}^{7} g(x) d x=4 \). Evaluate the following integrals. \( \int_{7}^{2} g(x) d x=-4 \) (Simplify your answer.) \( \int_{2}^{7} 5 g(x) d x=\square \) (Simplify your answer.)

Suppose \( \int^{4} f(x) d x=6, \int^{7} f(x) d x=-2 \), and \( \int^{7} g(x) d x=4 \). Evaluate the following integrals. \( \int_{7}^{2} g(x) d x=-4 \) (Simplify your answer.) \( \int_{2}^{7} 5 g(x) d x=20 \) 2 (Simplify your answer.) 7 \( \int_{2}[g(x)-f(x)] d x=6 \) 2 (Simplify your answer.) 7 \( \int_{2}[5 g(x)-f(x)] d x=\square \) (Simplify your answer.)