The value of a for which the equation `int_0^x sin^2(t/2)dt=a^2x^2-1/2(3x-1)+1/a^2` possess a solutio are:

The value of x for which the function f(x)=int_(0)^(x)(1-t^(2))e^(-t^(2)//2)dt has an extremum is

The total number of distinct x in[0,1] for which int_0^x t^2/(1+t^4) dt =2x-1 is

(i) If f(x) = int_(0)^(sin^(2)x)sin^(-1)sqrt(t)dt+int_(0)^(cos^(2)x)cos^(-1)sqrt(t) dt, then prove that f'(x) = 0 AA x in R . (ii) Find the value of x for which function f(x) = int_(-1)^(x) t(e^(t)-1)(t-1)(t-2)^(3)(t-3)^(5)dt has a local minimum.

Find the solution for x of the equation int_(2^(1/2))^x1/(t(t^2-1)^(1/2))dt= pi/2 .

find the range of values of t for which 2sin t=(1-2x+5x^(2))/(3x^(2)-2x-1)

Find the range of values of t for which 2sin t=(1-2x+5x^(2))/(3x^(2)-2x-1)

The solution for x of the equation int_(sqrt(2))^(x)(1)/(tsqrt(t^(2)-1))dt=(pi)/(2) , is

The solution for x of the equation int_(sqrt2)^(x)(dt)//t(sqrt(t^(2)-1))=(pi)/(2) is