What is #int_5^1(f(x)-2)dx#?

Question

If #int_1^5f(x)dx=20#, find #int_5^1(f(x)-2)dx#.

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Answer 1 · 2018-03-14T08:49:51

#-12#

#int_5^1(f(x)-2)dx#

#=int_5^1f(x)dx-int_5^1 2dx#

#=-int_1^5f(x)dx-[2x]_5^1#

#=-20-(2xx1-2xx5)#

#=-20- -8#

#=-12#