Mentor

## Definite integral

 Quote by Bread18 You still have to integrate it, perhaps evaluate would have been a better word, but either way, he now was to integrate $$\int^6_32f(x)-3dx$$
Evaluate is a better word, and that will involve substitution (i.e., replacing specific integrals by their known values). Integration is not a part of this problem. How could it be, since f(x) is not known?

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 Quote by Mark44 Integration is not a part of this problem. How could it be, since f(x) is not known?
Well, technically it still is, just not on f(x). You still have to integrate 3.
 All right, well this is probably wrong but here is what I got! I took out the 2, which I didn't I could do which is probably what confused me the most.. I'm having trouble with the symbols right now but I essentially put the 2 in front of the integral of the function and substracted the integral of 3. Which gave me 60-3x... Is that right??

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 Quote by lab-rat but I essentially put the 2 in front of the integral of the function and substracted the integral of 3.
That sounds right. So you rewrote your problem as $2 \int_{3}^6 f(x)dx - \int_{3}^6 3 dx$?

 Quote by lab-rat Which gave me 60-3x... Is that right??
The first part is fine, but the bolded part doesn't make any sense. If you're working with a definite integral...
 Yes that is how I wrote it. How should I solve the second part? I've been looking everywhere... The only thing I could find was that it's supposed to be the anti derivative.. Well 3x is the antiderivative of 3 isn't it?

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 Quote by lab-rat Yes that is how I wrote it. How should I solve the second part? I've been looking everywhere... The only thing I could find was that it's supposed to be the anti derivative.. Well 3x is the antiderivative of 3 isn't it?
Yes, so substitute the upper bound into that expression to get a value. Then substitute the lower bound into that expression to get a value. Then take the first value minus second value, and that's the definite integral.

Remember $\int_a^b f(x)dx = F(b) - F(a)$, where F(x) is the antiderivative of f(x).