Thread: how to integrate?

If a function f is defined by f(x) = S from 0 to x (1 / (1 + t^4)) dt, is f(1) = to 1/2?

I take it I have to integrate that thing, how do I do it?

Originally Posted by LeoBloom.

If a function f is defined by f(x) = S from 0 to x (1 / (1 + t^4)) dt, is f(1) = to 1/2?

I take it I have to integrate that thing, how do I do it?

we can say no without actually evaluating the integral.



By camparison the minimum of on [0,1] is 1/2 and the max is 1 so



equallity could only happen if the integrand was constant on [0,1]

I hope this helps.

Good luck.

Nope, sorry I didn't follow. I dont see how you get a min of 1/2 and a max of 1.

Originally Posted by LeoBloom.

Nope, sorry I didn't follow. I dont see how you get a min of 1/2 and a max of 1.

let







If your really want to be rigorous you could verify this with the first and second derivative test, but the function is postitive and decreasing for all t > 0 so its max is at the left end point and its min is at the right end point.

I hope this clears it up.