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Question-212314




Question Number 212314 by Spillover last updated on 09/Oct/24
Answered by mehdee7396 last updated on 09/Oct/24
f(x)=ln(((2−sinx)/(2+sinx)))  f(−x)=ln(((2+sinx)/(2−sinx)))=−f(x)  ⇒;f; is  ;odd⇒∫_(−(π/2)) ^(π/2) f(x)dx=0 ✓
f(x)=ln(2sinx2+sinx)f(x)=ln(2+sinx2sinx)=f(x);f;is;oddπ2π2f(x)dx=0
Answered by Ghisom last updated on 09/Oct/24
f(x)=ln ((2−sin x)/(2+sin x))  f(−x)=ln ((2+sin x)/(2−sin x)) =−ln ((2−sin x)/(2+sin x)) =−f(x)  ⇒ ∫_(−a) ^a f(x)dx=0
f(x)=ln2sinx2+sinxf(x)=ln2+sinx2sinx=ln2sinx2+sinx=f(x)aaf(x)dx=0

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