`a=3-2sqrt(2),f i n d t h e v a l u e o fa^2-1/(a^2)`

If sin(A-B)=1/(sqrt(10 ,))cos(A+B)=2/(sqrt(29)),fin dt h ev a l u eof2Aw h e r eAa n dBl i eb e t w e e n0a n dpi/4dot

f(x)=int_1^x(tan^(-1)(t))/t dtAAx in R^+,t h e nfin dt h ev a l u eof f(e^2)-f(1/(e^2))

If f(0)=1,f(2)=3,f(2)=5,t h e nfin dt h ev a l u eof int_0^1xf"(2x)dx

If S_n=sum_(r=1)^n r !(n >6),"t h e nf i n dt h ev a l u eo f" [cot^(-1)(cot(s_n-7[(S_n)/7]))],"w h e r e"[dot]"d e n o t e sg r e a t e s t" integer function

I fx+1/x=2,t h e p r i n c i p a l v a l u e o f sin^(-1)x is

Let C be a curve passing through M(2,2) such that the slope of the tangent at anypoint to the curve is reciprocal of the ordinate of the point. If the area bounded by curve C and lin x=2i s A ,t h e nt h e v a l u e of (3A)/2i s__

IfI_n=int_0^pix^nsinx dx ,t h e n fin d t h e v a l u eof I_5+20 I_3dot

IfI_n=int_x^pix^nsinx dx ,t h e n fin d t h e v a l u eof I_5+20 I_3dot

IfI_n=int_0^pix^nsinx dx ,t h e n fin d t h e v a l u eof I_5+20 I_3dot

Let f(0)=0a n dint_0^2f^(prime)(2t)e^(f(2t))dt=5.t h e nv a l u eoff(4)i s log 2 (b) log 7 (c) log 11 (d) log 13