You are Here: Home >< Maths

# Definite Integration Question watch

1. How can determine whether the area given by the integral is positive or negative? I tried sketching the graph and think it's positive but is there an algebraic way to prove this without actually doing the integration?
2. You're pretty much there. As is always positive in , what can we therefore deduce about its integral over that interval?
3. (Original post by FXLander)
How can determine whether the area given by the integral is positive or negative? I tried sketching the graph and think it's positive but is there an algebraic way to prove this without actually doing the integration?
Show that in the interval
4. (Original post by RDKGames)
Show that in the interval
What's the best way to do so? I know that cos 3x > 0 in the interval [0, pi/8], so does that mean sec 3x>0 in that interval as well?
5. (Original post by FXLander)
What's the best way to do so? I know that cos 3x > 0 in the interval [0, pi/8], so does that mean sec 3x>0 in that interval as well?
Yes. Since in that interval, all you're then doing to those values is taking their reciprocals, so they stay positive.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: October 21, 2017
Today on TSR

How do you think you'll do?

### University open days

Wed, 25 Jul '18
2. University of Buckingham
Wed, 25 Jul '18
3. Bournemouth University
Wed, 1 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams