Question

sin x2.dx

Answer 1

The function is given as,

y =  ∫ 0 π 2 sinx sinx + cosx dx (1)

From the property of integration,

∫ 0 b f( x ) dx= ∫ 0 b f( b−x ) dx

y=  ∫ 0 π 2 sin( π 2 −x ) sin( π 2 −x ) + cos( π 2 −x ) dx y= ∫ 0 π 2 cos( x ) cos( x ) + sin( x ) dx (2)

We have to add equations (1) and (2) to get the solution.

y+y= ∫ 0 π 2 sin( x ) sin ( x ) + cos ( x ) dx + ∫ 0 π 2 cos( x ) cos( x ) + sin( x ) dx 2y= ∫ 0 π 2 sin( x ) + cos( x ) cos( x ) + sin( x ) dx 2y= ∫ 0 π 2 1⋅dx 2y= π 2

Simplify further,

y= π 4

Thus, the value of the integral is π 4 .