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# Definite Integration

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1. Came across a question on definite integration and I'm not sure why it doesn't work

"Use integration to find giving your answer in the form a+b√3, where a and b are constants to be determined."

is what I got, and when subbing in √3 and 1, I get an answer as a long decimal instead of surd. Is there something wrong with the question or have I missed something?
2. (Original post by Rexx18)
Came across a question on definite integration and I'm not sure why it doesn't work

"Use integration to find giving your answer in the form a+b√3, where a and b are constants to be determined."

is what I got, and when subbing in √3 and 1, I get an answer as a long decimal instead of surd. Is there something wrong with the question or have I missed something?
Not sure how you can get a "long decimal" as the answer - you should be able to see just by looking at it that the answer's going to be a surd!

Post some working, then someone can see where you've gone wrong
3. (Original post by Rexx18)
Came across a question on definite integration and I'm not sure why it doesn't work

"Use integration to find giving your answer in the form a+b√3, where a and b are constants to be determined."

is what I got, and when subbing in √3 and 1, I get an answer as a long decimal instead of surd. Is there something wrong with the question or have I missed something?
When you sub in the values, you get:

Collect up all the rational parts, and note that . I'm uncertain as to what your issue is? Are you using a calculator? If so, don't. Use your head.
4. (Original post by Rexx18)
Came across a question on definite integration and I'm not sure why it doesn't work

"Use integration to find giving your answer in the form a+b√3, where a and b are constants to be determined."

is what I got, and when subbing in √3 and 1, I get an answer as a long decimal instead of surd. Is there something wrong with the question or have I missed something?
.... You used your calculator didn't you? use some workings out for subbing in
5. DId you use a calculator? I got 2/3 - 1/9 (root 3)
6. = 0.47422

Yeah, I did use a calculator for it
7. (Original post by Rexx18)
Came across a question on definite integration and I'm not sure why it doesn't work

"Use integration to find giving your answer in the form a+b√3, where a and b are constants to be determined."

is what I got, and when subbing in √3 and 1, I get an answer as a long decimal instead of surd. Is there something wrong with the question or have I missed something?
Your integration is correct.

You need to work it out manually I'm afraid. Your calculator will churn out a decimal if you put it all in. You may be able to calculate each individual term, but certainly not altogether.
8. Hmm, alright, this is the first def. integration question I've seen in which I can't use my calculator, thanks for the answers guys
9. (Original post by Rexx18)
Hmm, alright, this is the first def. integration question I've seen in which I can't use my calculator, thanks for the answers guys
What board are you doing? I am pretty sure you can't use your cacluator to integrate. You have to show your working. You can use the calc to add big integers/fractions but you generally you give answers in exact form.
10. Edexcel, I didn't mean I have one of those calculators that do integration for you, I meant that once you end up with the square brackets and limits, I sub in the limits into the equation all in one go to give me the answer, but in this case, it gave me a long decimal instead of the a+b√3 format
11. (Original post by Rexx18)
Edexcel, I didn't mean I have one of those calculators that do integration for you, I meant that once you end up with the square brackets and limits, I sub in the limits into the equation all in one go to give me the answer, but in this case, it gave me a long decimal instead of the a+b√3 format
But why would you do that when you can see just by looking that you're going to get a simple fraction plus a surd that's easy to rationalize?

You've made more work for yourself when all you needed after the integration was a bit of GCSE-level manipulation
12. Probably just a habit I guess, I tend to type in whatever I need using the Ans button, whether it's definite integration, numerical solutions in FP1 or anything like that, I find it much faster. But I guess I'll work it out without a calculator if it asks for the answer in surd format

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