what is the integral of sin(x^2)

Question

substitute x^2 for x and integrate from 0 to 1

Answer 1

Given  int sin^2x

from ....cos2x=cos^2x-sin^2x

cos2x=[1-sin^2x]-sin^2x

=1-2sin^2x

sin^2x=1/2[1-cos2x]

int sin^2x=int 1/2[1-cos2x]dx

1/2int1 dx-1/2int cos2x dx

x/2-[sinx]/2

[x-sinx]/2

int sin^2x=[x-sinx]/2