Find the integral of \sin(x^{2})

elvishwitchxyp

elvishwitchxyp

Answered question

2021-12-10

Find the integral of sin(x2)

Answer & Explanation

recoronarrv

recoronarrv

Beginner2021-12-11Added 20 answers

Substitute u=2×xπ
dx=π2×du
sin(x2)×dx
=π2sin(π×u22)×du
This is special integral Fresnel integral =S(u)
π2sin(π×u22)×du=π×S(u)2
=π×S(2×xπ)2+C if we undo the substitution.
Mary Herrera

Mary Herrera

Beginner2021-12-12Added 37 answers

sin(x2)dx=π2S(2πx)=π2S(2πx)+C

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