Use the form of the definition of the integral given in the theorem to evaluate the integral. 8 (x2 − 4x + 9) dx 1

Answer:[tex]\displaystyle \int\limits^8_1 {(x^2 - 4x + 9)} \, dx = \frac{32452}{5}[/tex]General Formulas and Concepts:CalculusIntegrationIntegralsIntegration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]Step-by-step explanation:Step 1: DefineIdentify[tex]\displaystyle \int\limits^8_1 {(x^2 - 4x + 9)} \, dx[/tex]Step 2: Integrate[Integral] Rewrite [Integration Property - Addition/Subtraction]:               [tex]\displaystyle \int\limits^8_1 {(x^2 - 4x + 9)} \, dx = \int\limits^8_1 {x^2} \, dx - \int\limits^8_1 {4x} \, dx + \int\limits^8_1 {9} \, dx[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]:               [tex]\displaystyle \int\limits^8_1 {(x^2 - 4x + 9)} \, dx = \int\limits^8_1 {x^2} \, dx - 4\int\limits^8_1 {x} \, dx + 9\int\limits^8_1 {} \, dx[/tex][Integrals] Reverse Power Rule:                                                                  [tex]\displaystyle \int\limits^8_1 {(x^2 - 4x + 9)} \, dx = \frac{x^3}{3} \bigg| \limits^8_1 - 4 \bigg( \frac{x^2}{2} \bigg) \bigg| \limits^8_1 + 9(x) \bigg| \limits^8_1[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:           [tex]\displaystyle \int\limits^8_1 {(x^2 - 4x + 9)} \, dx = \frac{511}{3} - 4 \bigg( \frac{63}{2} \bigg) + 9(7)[/tex]Simplify:                                                                                                         [tex]\displaystyle \int\limits^8_1 {(x^2 - 4x + 9)} \, dx = \frac{32452}{5}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)Unit: Integration