Calculate the intergral of [cos(x^2)] from -pi/4 to pi/4?

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Calculate the intergral of [cos(x^2)] from -pi/4 to pi/4?

Anyone can help me calculate the integral of [cos(x^2)] from -pi/4 to pi/4 . Any help is appreciated, thanks!!

2007-10-25 02:29:54 · 3 answers · asked by Mamichiyo 3 in Science & Mathematics ➔ Mathematics

3 answers

I don't think this can be done analytically. Only by numerical methods.

2007-10-25 03:30:21 · answer #1 · answered by Steiner 7 · 0⤊ 1⤋

Assume it is integral of cos Â² x that is required.
I = â« cos Â² x dx between given limits.
I = â« (1/2) cos 2x + 1 / 2 dx
I = (1/4) sin 2x + (1/2) x

Inserting limits:-
(1/4) sin Ï/2 + (1/2) Ï/4
- (1/4) sin(-Ï/2) - (1/2) (-Ï/4)

= (1/4) + Ï/8 + (1/4) + Ï/8
= (1/2) + Ï/4

2007-10-29 16:10:09 · answer #2 · answered by Como 7 · 1⤊ 0⤋

cosx^2=cos2x+1

u can easily integrate this function

2007-10-25 09:34:23 · answer #3 · answered by Anonymous · 0⤊ 2⤋