Calc1.79

From Example Problems
Jump to: navigation, search

Find the average value of the function 2sec^{2}x on the interval \left[0,{\frac  {\pi }{4}}\right].

Find the total value of the function on the interval by taking the integral. Then divide this value by the length of the interval to find the average value of the function on the interval. So, the average value is

{\frac  {1}{{\frac  {\pi }{4}}-0}}\int _{{0}}^{{{\frac  {\pi }{4}}}}2\sec ^{2}x\,dx={\frac  {4}{\pi }}\left[2\tan x\right]_{{0}}^{{{\frac  {\pi }{4}}}}={\frac  {8}{\pi }}[1-0]={\frac  {8}{\pi }}\,


Main Page : Calculus