Asked by Anonymous
0 to 1/2∫(sin(x^2))dx
Answers
Answered by
Reiny2
Recall that
sin^2 x = 1/2 - (1/2)cos (2x)
so...
∫(sin(x^2))dx from 0 to 1/2
= ∫(1/2 - (1/2)cos (2x) dx from 0 to 1/2
= x/2 - (1/4)sin (2x) from 0 to 1/2
= ......
sin^2 x = 1/2 - (1/2)cos (2x)
so...
∫(sin(x^2))dx from 0 to 1/2
= ∫(1/2 - (1/2)cos (2x) dx from 0 to 1/2
= x/2 - (1/4)sin (2x) from 0 to 1/2
= ......
Answered by
oobleck
you cannot integrate sin(x^2) using elementary functions.
Some numeric method is needed, or one of the special functions defined as integrals. In this case, the Fresnel Integral.
Some numeric method is needed, or one of the special functions defined as integrals. In this case, the Fresnel Integral.