1a small editing bro.!
put tan-1x (or arc tanx)=t. and the rest of the solution is same.
I1=∫(x/sinx)
int frm 0 to pi/2
I2=∫arc tanx/x
int frm 0 to 1
then I1/I2 =?
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8 Answers
1357I2=∫arc tanx/x
int frm 0 to 1
put arctanx=t
I2=(0 to π/4)∫t.sec2tdt/tant=∫t/sintcost=∫2tdt/sin2t
put 2t=x it becomes (0 to pi/2)∫x/sinx
1
11.) I= 0∫Π/2 x/sinx dx
=> I= 1/2 0∫Πx/sinx dx -------#1
=> I=1/2 0∫ΠΠ-x/sinx dx ----------#2
adding #1` and #2,
2I = 0∫ΠΠdx => I =Π2/2.
