Evaluate the integral?

Question

Evaluate #int_0^pif(x)dx# where
f(x)= piecewise sin(x) if 0 #<=# x #<=# #pi/2# and x if #pi/2# #<=# x #<=# #pi#

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Answer 1 · 2018-04-26T06:33:14

#int_0^pif(x)dx#

#=int_0^(pi/2)sin(x)\ dx+int_(pi/2)^(pi)x\ dx#

#=[-cos(x)]_0^(pi/2)+[1/2x^2]_(pi/2)^pi#

#=1+3/8pi^2#