Integeration

IF sin x is the integerating factor (I.F ) of the linear differential equation (dy)/(dx) +py =Q then P is

Let f(x) be a continuous function such that int_(n)^(n+1) f(x) dx=n^(3) , ninZ . Then the value of the integeral int_(-3)^(3) f(x) dx, is

Find the number of positive integeral solution of the inequation x+y+z >=150, where 0 , x le 60, 0 < y le 60, 0 < z le 60.

A squence of positive terms A_(1),A_(2),A_(3),"....,"A_(n) satisfirs the relation A_(n+1)=(3(1+A_(n)))/((3+A_(n))) . Least integeral value of A_(1) for which the sequence is decreasing can be

If number of integeral values of 'm' for which exactly one root of the equation. x^(2)+3mx+m^(2)-4=0 lies on the interval (-6, 2) is k. Then [(k)/(5)] = (where [.] denote greatest integer function).

The least positive integeral value of real lambda so that the equation (x-a)(x-c)(x-e)+lambda (x-b)(x-d)=0, (a gt b gt c gt d gt e) has distinct real roots is __________.

If [*] denots the greatest integer function then the value of the integeral int_(-pi//2)^(pi//2)([(x)/(pi)]+0.5) dx , is

The solution set of the equation [x]^(2) +[x+1] -3=0, where [.] represents greatest integeral function is :