Question

(1) $\int 1 - x ^ { 2 } d x =$

Explanation:

Step1: Use integral formula

$$\int 1dx-\int x^{2}dx$$

Step2: Integrate term - by - term

$$\int 1dx=x+C_1,\int x^{2}dx=\frac{x^{3}}{3}+C_2$$

Step3: Combine results

$$x-\frac{x^{3}}{3}+C$$ ($C = C_1 - C_2$ is the constant of integration)

Answer:

$$x-\frac{x^{3}}{3}+C$$