If `f(x)=sinx ,AAx in [0,pi/2],f(x)+f(pi-x)=2,AAx in (pi/2,pi]a n df(x)=f(2pi-x),AAx in (pi,2pi],` then the area enclosed by `y=f(x)` and the x-axis is
(a)`pi` sq `dot` units
(b) `2pi` sq `dot` units
(c) `2` sq `dot` units
(d) `4`sq `dot` units

If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int_0^(pi/2)f(x)f(pi/2-x)dx=int_0^pif(x)dx

If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int_0^(pi/2)f(x)f(pi/2-x)dx=int_0^pif(x)dx

The area of a circle whose area and circumference are numerically equal, is (a) 2pi sq. units (b) 4pi sq. units (c) 6pi sq. units (d) 8pi sq. units

Area enclosed by the curve (y-sin^(- 1)x)^2=x-x^2 , is (A) pi/2 sq.units (B) pi/4 sq.units (C) pi/8 sq.units (D) none of these

If f'(x)=x|sinx|AAx""in(0,pi/2)andf(0)=(1)/(sqrt3), then f(x) will be

If int_0^pi x f(sinx) dx=A int_0^(pi/2) f(sinx)dx , then A is (A) pi/2 (B) pi (C) 0 (D) 2pi

For f(x)=sin^2x ,x in (0,pi) point of inflection is: pi/6 (b) (2pi)/4 (c) (3pi)/4 (d) (4pi)/3

If f(x)=|cosx-sinx| ,find f^(prime)(pi/6) and f^(prime)(pi/3)dot

Show that 0

Consider a function f defined by f(x)=sin^(-1) sin ((x+sinx)/2) AA x in [0,pi] which satisfies f(x)+f(2pi-x)=pi AA x in [pi, 2pi] and f(x)=f( 4pi-x) for all x in [2pi,4pi] then If alpha is the length of the largest interval on which f(x) is increasing, then alpha =