Is There a Way to Fix Unbalanced Parentheses in a Function?

[Compaq]

Let's say one has a function y=sqrt(5+(cos(x)^5), and that one must find the integral: lower limit=2 and upper limit=7x².

Is this function defined on a closed interval [2,7x²], or is this function in fact not defined at all, as 7x² isn't a specific limit?

-Compaq

 

[mathman]

The function is defined. 7x² is a perfectly valid upper limit. Just be careful to replace x in the integrand with another symbol to avoid confusion.

 

[Compaq]

The function is defined. 7x² is a perfectly valid upper limit. Just be careful to replace x in the integrand with another symbol to avoid confusion.

So if I were to calculate the mentioned integral, int y, and then find dy/dx, I could just use the fundamental theorem of Calculus and say that if the function is continuous, which it is in the defined interval, and that since y(t)=Y(t), Y'(t)= y(t)..

hmm, that was badly formulated, but I hope you see what I mean. No need to spend time doing hard integrals manually, as it's normally done numerical anyways, when I can just say that the derivative of the integral equals the thing I started with in the beginning?

I know, not very mathematically formulated... I'm new that this! :P

 

[mathman]

Let F(x) be the integral, then F'(x)=y(7x²)14x.

 

[g_edgar]

y=sqrt(5+(cos(x)^5)

Unbalanced parentheses are never good.