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.
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