Question

Find the indefinite integral. (remember to use absolute values where appropriate. use c for the constant of integration.) x2 − 22x dx

Answer 1

`\displaystyle \int {(x^2 - 22x)} \, dx = (x^3)/(3) - 11x^2 + C`

General Formulas and Concepts:

Calculus

Integration

• Integrals
• [Indefinite Integrals] Integration Constant C

Integration Rule [Reverse Power Rule]:
`\displaystyle \int {x^n} \, dx = (x^(n + 1))/(n + 1) + C`

Integration Property [Multiplied Constant]:
`\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx`

Integration Property [Addition/Subtraction]:
`\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx`

Explanation:

Step 1: Define

Identify

`\displaystyle \int {(x^2 - 22x)} \, dx`

Step 2: Integrate

1. [Integral] Rewrite [Integration Property - Addition/Subtraction]:
   `\displaystyle \int {(x^2 - 22x)} \, dx = \int {x^2} \, dx - \int {22x} \, dx`
2. [2nd Integral] Rewrite [Integration Property - Multiplied Constant]:
   `\displaystyle \int {(x^2 - 22x)} \, dx = \int {x^2} \, dx - 22\int {x} \, dx`
3. [Integrals] Reverse Power Rule:
   `\displaystyle \int {(x^2 - 22x)} \, dx = (x^3)/(3) - 22 \Big( (x^2)/(2) \Big) + C`
4. Simplify:
   `\displaystyle \int {(x^2 - 22x)} \, dx = (x^3)/(3) - 11x^2 + C`

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration