Let f(x)>0 be a continuous function such that the area bounded by the curve y=f(x),x -axis and the lines x=0 and `x=lambda` is +`(lambda^(2))/(2)+cos^(2)lambda` .Then `f((pi)/(4))` is

Let f(x) be a continuous function such that the area bounded by the curve y=f(x), the x-axis, and the lines x=0 and x=a is 1+(a^(2))/(2)sin a. Then,

Let f (x) be a continous function such that the area bounded by the curve y =f (x) x-axis and the lines x=0 and x =a is (a ^(2))/( 2) + (a)/(2) sin a+ pi/2 cos a, then f ((pi)/(2)) is

Area bounded by the curve f(x)=cos x which is bounded by the lines x=0 and x=pi is

Let f(x) be a non-negative continuous function such that the area bounded by the curve y=f(x), the x-axis, and the ordinates x=(pi)/(4) and x=betagt(pi)/(4)" is "beta sin beta +(pi)/(4)cos beta +sqrt(2)beta. Then f'((pi)/(2)) is

Let f be a non-negative continuous function such that the area bounded by the curve y = f(x), x-axis and the coordinates x = 3:sqrt2 and x = beta > pi/4 is (beta sin beta + pi/4 cos beta + sqrt2 beta). then f(pi/2) is:

Let f be a continuous function such that fx)>0,AA x and area boundey by y=f(x)= axis and the line x-a (where a is a parameter) is e^(a^(2))-1. then f(x) is

Let f(x) be continuous function such that f(0)=1,f(x)-f((x)/(7))=(x)/(7)AA x in R. The area bounded by the curve y=f(x) and the coordinate axes is

Let f(x) be a continuous and positive function, such that the area bounded by y=f(x), x - axis and the lines x^(2)=2ax is 6a^(2)+sina(AA a gt 0) sq. units. If f(pi)=kpi , then the value of k is equal to

Let f(x) be a continuous function such that int_(-2)^(2)f(x)dx=0 and int_(0)^(2)f(x)dx=2. The area bounded by y=f(x) , x -axis, x=-2 and x=2 is