Upper and Lower bounds... Conceptual

**ebonyscythe** · December 3rd 2007, 12:35 PM

Suppose we know that $1 \le \int_{0}^{4} g(x)dx \le 10$ . Determine the best possible upper and lower bounds for $\int_{0}^{2} xg(x^2)dx$ that can be deduced from this information. Justify your answer.

Again, I've no idea where to really start on this one... if someone could help me through it I'd appreciate it.

**Jhevon** · December 3rd 2007, 01:41 PM

Originally Posted by ebonyscythe

Suppose we know that $1 \le \int_{0}^{4} g(x)dx \le 10$ . Determine the best possible upper and lower bounds for $\int_{0}^{2} xg(x^2)dx$ that can be deduced from this information. Justify your answer.

Again, I've no idea where to really start on this one... if someone could help me through it I'd appreciate it.

this is a substitution problem cleverly disguised. try the substitution u = x^2 (remember to change the limits also) and see what you get

**angel.white** · December 3rd 2007, 01:49 PM

Is it between .5 and 5?

**Jhevon** · December 3rd 2007, 01:53 PM

Originally Posted by angel.white

Is it between .5 and 5?

yes. inclusive, of course

good job

**angel.white** · December 3rd 2007, 02:08 PM

Originally Posted by Jhevon

yes. inclusive, of course

good job

Appreciate it, yesterday I didn't even know about changing the interval O.o

It's amazing how I learn so much more from reading through questions on this site, than from studying my book.

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