`T h ev a l u eof(pi^2)/(1n3)int_(7/6)^(5/6)sec(pix)dxi s____`

T h ev a l u eofint_(-2)^2|1-x^2|dxi s_______

A function is reprersented parametrically by the equations x=(1+t)/(t^3); y=3/(2t^2)+2/tdotT h e nt h ev a l u eof|(dy)/(dx)-x((dy)/(dx))^3| is__________

T h ev a l u eofint_0^1(2x^2+3x+3)/((x+1)(x^2+2x+2))dxi s pi/4+2log2-tan^(-1)2 pi/4+2log2-tan^(-1)1/3 2log2-cot^(-1)3 (d) -pi/4+log4+cot^(-1)2

T h ev a l u eofint_(-2)^1[x[1+cos((pix)/2)]+1]dx , where [.] denotes the greatest integer function, is 1 (b) 1//2 (c) 2 (d) none of these

Iff(x)=x+int_0^1t(x+t)f(t)dt ,t h e nt h ev a l u eof(23)/2f(0) is equal to _________

T h ev a l u eofint_1^((1+sqrt(5))/2)(x^2+1)/(x^4-x^2+1)log(1+x-1/x)dxi s (a) pi/8(log)_e2 (b) pi/2(log)_e2 (c) -pi/2(log)_e2 (d) none of these

The value of int_(1/e)^(tanx)(tdt)/(1+t^2)+int_(1/e)^(cotx)(dt)/(t(1+t^2)), where x in (pi/6,pi/3) , is equal to: (a)0 (b) 2 (c) 1 (d) none of these

Evaluate: int_(pi//6)^(pi//3)(dx)/(1+sqrtcotx)

: If f(x)={x^2+2,xgeq2 1-x ,x 1, 3-x , xlt=0,t h e nt h ev a l u eoflim_(x->1)f(g(x))i s__

The value of int_0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dxi s