If k be positive integer , then the number of values of k satisfying `int_0^(pi/2)[k^2(cos3x+1/2cosx)+sinx-2kcosx]dxlt=1` is

If a is a positive integer, then the number of values of a satisfying int_0^(pi/2){a^2((cos3x)/4+3/4cosx)+asinx-20cosx}dx<=a^2/3 is:

If a is positive integer then the number of values of 'a' satisfying int_(0)^(pi//2) {a^(2)((cos3x)/(4)+(3)/(4)cosx)+a sin x-20cosx} dx le (a^(2))/(3) are

If a is a positive integer,then the number of values of a satisfying int_(0)^((pi)/(2)){a^(2)(cos3(x)/(4)+(3)/(4)cos x)+a sin x-20cos x}dx<=(a^(2))/(3) is:

int_0^(pi/2) (cosx-sinx)/(1+sinx cosx) dx =

If n is a positive integer and (1+i)^(2n)=k cos(n pi/2) , then the value of k is

Write the value of int_0^(pi/2)(sinx)/(sinx+cosx)dx-int_0^(pi/2)(cosx)/(sinx+cosx)dx