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B
I=e√2−e
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C
ln(I+e)=√2
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D
I is a rational number
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Solution
The correct options are AI is an irrational number BI=e√2−e Cln(I+e)=√2 I=∫π4−π4esecx|sinx|sec2xdx(1+esinx)... (1) Using ∫baf(x)dx=∫baf(a+b−x)dx I=∫π4−π4esecx|sinx|sec2xdx(1+e−sinx)... (2) Add (1) & (2) 2I=∫π4−π4esecx|sinx|sec2xdxI=∫π40esecxsecxtanxdx esecx=tI=∫e√2edt=e√2−e