Integral of f(x)=cos(x)/sqrt(1+x^2) - Get Help Here!

[dvdstvns]

I need to solve for the integral of f(x)=cos(x)/sqrt(1+x^2)
Integral calculating computers online all say that this integral doesn't exist or takes too much computing time to solve. This is only a calculus 1 problem so I imagine if the answer is too complicated then it was probably a mistake on the professors part. Any help is greatly appreciated.

 

[DrewD]

Is the question asking for the indefinite or definite integral? I would guess that there is a typo if the only statement of the problem is $\int\frac{\cos x}{\sqrt{1+x^2}}$

 

[dvdstvns]

The full problem is:
True or false 0≤∫^1_-1 cos(x)/√1+x²

Mod edit: In a nicer format, this is
$$0 \leq \int_{-1}^1 \frac{cos(x)~dx}{\sqrt{1 + x^2}}$$

 

[disregardthat]

How does cos(x)/√1+x2 look like in the interval [-1,1]? Is it positive or negative? You can perhaps conclude something based on that.

 

[dvdstvns]

Well I know the answer to the problem is true, however, I'm trying to show the integral to show work, and I have no idea how to get the integral.

 

[Mark44]

Well I know the answer to the problem is true, however, I'm trying to show the integral to show work, and I have no idea how to get the integral.

You don't need to evaluate the integral to answer the question. In fact, you won't be able to evaluate the integral, either. The hint from disregardthat is a good place to start.

 

[MarneMath]

As Mark44 stated you won't solve this problem by solving this integral =(. Any decent calculus book should give you some useful properties of definite integrals and when order may be preserved. Apply that information to the hint, and you should be good to go!