Evaluate integral

[janeann]

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

 

[galactus]

\(\displaystyle \int\frac{cos(x)}{sin^{2}(x)+1}dx\)

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

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

 

[mmm4444bot]

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

Typing sin(x)^2 does.

 

[Deleted member 4993]

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.

 

[galactus]

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

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

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

There are ways to evaluate \(\displaystyle \int_{0}^{\frac{\pi}{2}}sin(x^{2})\), though.

 

[janeann]

Thank you!

 

[Deleted member 4993]

So which one was it .... sin(x[sup:1hori25u]2[/sup:1hori25u]) or sin[sup:1hori25u]2[/sup:1hori25u](x) ????

 

[janeann]

sorry it was sin^2(x)