Answer to Question #162031 in Calculus for Phyroe

Question

Evaluate the the integral of (2x+1)^7 dx from-½ to ½

Answer 1

$\begin{array}{l} \int\limits_{ - \frac{1}{2}}^{\frac{1}{2}} {{{\left( {2x + 1} \right)}^7}} dx = \frac{1}{2}\int\limits_{ - \frac{1}{2}}^{\frac{1}{2}} {2{{\left( {2x + 1} \right)}^7}} dx = \frac{1}{2}\int\limits_{ - \frac{1}{2}}^{\frac{1}{2}} {{{\left( {2x + 1} \right)}^7}} d(2x + 1) = \left. {\frac{{{{\left( {2x + 1} \right)}^8}}}{{16}}} \right|_{ - \frac{1}{2}}^{\frac{1}{2}} = \\ = \frac{{{{\left( {1 + 1} \right)}^8} - {{( - 1 + 1)}^8}}}{{16}} = 16 \end{array}$

Answer: 16