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Definite Integration

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?

Reply 1

davros

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 :smile:

Reply 2

Zacken

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:

\frac{(\sqrt{3})^4}{24} - \frac{1}{3\sqrt{3}} - \frac{1}{24} + \frac{1}{3 \times 1}

Collect up all the rational parts, and note that

\frac{1}{3\sqrt{3}} = \frac{1}{9} \cdot \sqrt{3}

. I'm uncertain as to what your issue is? Are you using a calculator? If so, don't. Use your head.

Reply 3

thefatone

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

\sqrt 3

Reply 4

SirRaza97

DId you use a calculator? I got 2/3 - 1/9 (root 3)

Reply 5

Rexx18

= 0.47422

Yeah, I did use a calculator for it

Reply 6

oinkk

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.

Reply 7

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

Reply 8

SirRaza97

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.

Reply 9

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

Reply 10

davros

Original post by Rexx18

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 :smile:

Reply 11

Rexx18

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