`IfI_n=int_0^1(1-x^5)^n dx ,t h e n(55)/7(I_(10))/(I_(11))i se q u a lto___`

If I_n=int( lnx)^n dx then I_n+nI_(n-1)

IfI_n=int_0^pie^x(sin"x")^("n")dx ,t h e n(I_3)/(I_1)"is equal to" 3/5 (b) 1/5 (c) 1 (d) 2/5

L e tI_1=thetaint_0^1(e^xdx)/(1+x)a n dI_2thetaint_0^1(x^2dx)/(e^x^3(2-x^3))dott e h n(I_1)/(I_2)i se q u a lto 3/e (b) e/3 (c) 3e (d) 1/(3e)

Let f be a positive function. Let I_1=int_(1-k)^k xf([x(1-x)])dx , I_2=int_(1-k)^kf[x(1-x)]dx ,w h e r e2k-1> 0. T h e n(I_1)/(I_2)i s 2 (b) k (c) 1/2 (d) 1

"I f"I_1=int_(-100)^(101)(dx)/((5+2x-2x^2)(1+e^(2-4x))) "and"I_2=int_(-100)^(101)(dx)/(5+2x-2x^2),t h e n(I_1)/(I_2)"i s" (a)2 (b) 1/2 (c) 1 (d) -1/2

IfI_n=int_0^1x^n(tan^(-1)x)dx ,t h e np rov et h a t (n+1)I_n+(n-1)I_(n-2)=-1/n+pi/2

If U_n=int_0^1x^n(2-x)^ndxa n dV_n=int_0^1x^n(1-x)^n dx ,n in N , and if (V_n)/(U_n)=1024 , then the value of n is________

Let I_(n)=int_(0)^(1)x^(n)sqrt(1-x^(2))dx. Then lim_(nrarroo)(I_(n))/(I_(n-2))=

Ifx=int_c^(sint)sin^(-1)z dz ,y=int_k^(sqrt(t))(sinz^2)/zdz ,t h e n(dy)/(dx)i se q u a lto (tant)/(2t) (b) (tant)/(t^2) (c) tan t/(2t^2) (d) (t a tt^2)/(2t^2)

For x in R and a continuous function f, let I_1=int_(s in^2t)^(1+cos^2t)xf{x(2-x)}dxa n dI_2= int_(sin^2t)^(1+cos^2)xf{x(2-x)}dxdotT h e n(I_1)/(I_2) is -1 (b) 1 (c) 2 (d) 3