解答题
15.设f(x)=f(x-π)+sinx，且当x∈[0，π]时，f(x)=x，求∫π3πf(x)dx．
【正确答案】∫π3πf(x)dx=∫π3π[f(x-π)+sinx]dx=∫π3πf(x-π)dx+∫π3πsinxdx
=∫02πf(x)dx=∫0πxdx+∫π2πf(x)dx=
+∫π2π[f(x-π)+sinx]dx
=
+∫π2πf(x-π)dx+∫π2πsinxdx=
=∫02πf(x)dx=∫0πxdx+∫π2πf(x)dx=
+∫π2π[f(x-π)+sinx]dx=
+∫π2πf(x-π)dx+∫π2πsinxdx=【答案解析】