Question

f（x）＝In（1+x）x>0,f（x）＝1/1+x^2 x<=0求∫2→0f(x-1)dx

Answer 1

问：f（x）＝In（1+x）x>0,f（x）＝1/1+x^2 x<=0求∫2→0f(x-1)dx

答：f（x）＝In（1+x）x>0,f（x）＝1/1+x^2 x<=0求∫2→0f(x-1)dx=π/4+2ln2-1

答：当x∈[0,1], x-1∈[-1,0]所以f(x-1)=1/1+(x-1)²，当x∈[1,2]时，x-1∈[0,1]，f(x-1)=lnx

答：所以∫2→0f(x-1)dx=∫0到1[1/1+(x-1)²]dx+∫1到2(lnx)dx=arctan(x-1)|0到1+(xlnx-x)|1到2=π/4+2ln2-1

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