`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`

x=y ln(xy),t h e n

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__

If I_(n)=int_(0)^(1)x^(n)e^(-x)dx for n in N, then I_(7)-I_(6)=

If I_(n)=int x^(n)e^(x)dx, then I_(5)+5I_(4)=

Statement-1: int_(0)^(npi+v)|sin x|dx=2n+1-cos v where n in N and 0 le v lt pi . Stetement-2: If f(x) is a periodic function with period T, then (i) int_(0)^(nT) f(x)dx=n int_(0)^(T) f(x)dx , where n in N and (ii) int_(nT)^(nt+a) f(x)dx=int_(0)^(a) f(x) dx , where n in N

IfI_(n)=int_(0)^( pi)e^(x)(sin x)^(n)dx,then(I_(3))/(I_(1)) is equal to (3)/(5)(b)(1)/(5)(c)1(d)(2)/(5)

If I_(n)=int_(1)^(e)(log x)^(n) d x, then I_(n)+nI_(n-1) equal to

If I_(n)=int_(0)^( pi)e^(x)(sin x)^(n)dx, then (I_(3))/(I_(1)) is equal to

l_(1)=(d)/(dx)(e^(tanx)) l_(2)=lim_(h to 0)(e^(sin(x+h)-e^(sinx)))/(h) l_(3)=inte^(sinx)cosxdx , then which one of the following is correct ?