QuestionEnter your answer as a fraction or as a number rounded to three decimal places. Find the area bounded by the graphs of $y=x^{2}$ and $y=32-x^{2}$ for $0 \leq x \leq 9$. Area = $\square$

Studdy Solution
Calculate the definite integrals:
$$\text{Area} = (32 \times 4 - 32 \times 0) - \left( \frac{2}{3}(4)^3 - \frac{2}{3}(0)^3 \right)$$
$$\text{Area} = 128 - \frac{2}{3}(64)$$
$$\text{Area} = 128 - \frac{128}{3}$$
$$\text{Area} = \frac{384}{3} - \frac{128}{3}$$
$$\text{Area} = \frac{256}{3}$$
The area bounded by the graphs is:
$$\boxed{\frac{256}{3}}$$