### Home > APCALC > Chapter 4 > Lesson 4.2.4 > Problem4-83

4-83.

Chang Young is attempting to evaluate the following integral: $\int _ { 1 } ^ { 5 } ( 5 x + 2 ) d x$.
He writes the following steps:

$\left. \begin{array} { l } { \frac { 5 } { 2 } 5 ^ { 2 } + 2 ( 5 ) + C - \frac { 5 } { 2 } 1 ^ { 2 } + 2 ( 1 ) + C } \\ { \frac { 5 } { 2 } \cdot 25 + 10 + C - \frac { 5 } { 2 } + 2 + C } \\ { \frac { 125 } { 2 } - \frac { 5 } { 2 } + 12 + 2 C } \\ { \frac { 120 } { 2 } + 12 + 2 C } \\ { 60 + 12 + 2 C } \\ { 72 + 2 C } \end{array} \right.$

He knows that this is a definite integral and there should not be any $C$s in his answer. Also, the answer key says the answer is $68$. He needs your help to find his error and figure out how to eliminate his $+ 2C$.

His error is in the first line. How does he use or not use the Distributive Property?