Evaluate integral

janeann

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Integrate (cos(x))/(1+sin(x^2))dx from 0 to pi/2. Use Fundamental Theorem of Calculus to evaluate.
 
cos(x)sin2(x)+1dx\displaystyle \int\frac{cos(x)}{sin^{2}(x)+1}dx

Let u=sin(x),   du=cos(x)dx\displaystyle u=sin(x), \;\ du=cos(x)dx

Make the subs and it results in an integral involving arctan.
 


Typing sin(x^2) does not mean sin(x)*sin(x).

Typing sin(x)^2 does.

 
janeann said:
Integrate (cos(x))/(1+sin(x^2))dx from 0 to pi/2. Use Fundamental Theorem of Calculus to evaluate.

There are two FTCs - which one is applicabble for this problem?

Please share your work withus, indicating exactly where you are stuck - so that we may know where to begin to help you.
 
janeann said:
Integrate (cos(x))/(1+sin(x^2))dx from 0 to pi/2. Use Fundamental Theorem of Calculus to evaluate.

I assumed you meant sin2(x)\displaystyle sin^{2}(x) and not sin(x2)\displaystyle sin(x^{2}).

These are two different animals. The latter is not integrable in the elementary sense and would require numerical methods.

There are ways to evaluate 0π2sin(x2)\displaystyle \int_{0}^{\frac{\pi}{2}}sin(x^{2}), though.
 
So which one was it .... sin(x[sup:1hori25u]2[/sup:1hori25u]) or sin[sup:1hori25u]2[/sup:1hori25u](x) ????
 
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