## anonymous 3 years ago Integral help?

1. anonymous

Show that the value of ∫ (from 0 to 1) $\sqrt{x+8}dx$ lies between 2$\sqrt{2}$ amd 3.

2. anonymous

2sqrt2 and 3. sorry idk why it is formatting the text like that.

3. Goten77

so i take it instead of doing the integral.. they want the proof method.... i can try and sum it up

4. anonymous

the theorems? like if it's even or odd?

5. Goten77

|dw:1359001517057:dw|

6. Goten77

so we know that this shaded area is almost a rectangle... and that area is BH but the B=1 so its just the H that matters.... which is between sqrt of 8 and 3......

7. Goten77

that last part i meant sqrt(8) and 3 the area is between one of those 2 because this shape has a little slop on the top so it is just a little bigger then the sqrt(8) but also less then 3.... does this make sense? |dw:1359001866185:dw|

8. anonymous

yea i see that from f(0) and f(1), the values are between 2.8 and 3, but i have trouble putting it into integral form? :(

9. Goten77

putting it in integral form? you mean like actually solving it? i can show you how

10. anonymous

well i think that it's asking me to write a proof or to explain it in calculus... i kinda forgot the word for it lol

11. anonymous

i think it's like boundaries?

12. Goten77

yes it has boundaries and limits to what its area is restricted to

13. anonymous

i think it's asking me to write the boundaries in integral form.. like 2.8 < integral from 0, 1... < 3. i don't know where to start lol!

14. Goten77

aah... proofs are annoying... but as long as it makes sense its ok... if u have other "real" problems ied do those 1st... generally proofs are just long explanations .... and by real problems i mean were you can do work and get a answer.. proofs are just explaining calculus to some1 who hasnt taken it... and thats really hard... but eh i think u get it and thats all that matters

15. anonymous

yea lol! i understand it, but i have trouble putting it into a "calculus sentence" or whatever they call it lol. i understand the area is between the 2.8 and 3 but i'm not sure how to translate it lol