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(edited 6 years ago)

I have been having issues with a few problems: I get the answer right, but the accuracy is wrong (this is not to do with significant figures or decimal points, that's more or less figured out now).

Here is a simple integration that will act as an example:

\int^2_1 (8/x^5 + 3/\sqrt x)

The answer I got is 4.3603, but the textbook answer is -33/8 + 6

\sqrt 2

.

To 5 significant figures, my answer is still equal to that of the textbook, but afterwards mine is...less accurate.

The difference in how the solution was worked out lies in simplification of coefficients of x: I simplified the coefficients of x as far as possible (i.e. 8x^-5 + 3x^-1/2). The textbook solution on the other hand integrated the square roots directly, without converting into a more easily integrable form.

There's nothing wrong with leaving the integrand as 8x^-5 + 3x^(-1/2), but I don't see why you would need to give the answer as a decimal unless specifically required. Leaving it as a surd or fraction is alot easier to deal with imo and allows you to check your answer alot more easily.

Reply 2

sammychu00

Can you show me your working out? I just tried the question using the simplified coefficients and got the same answer as the textbook, so it's probably something to do with your working out.

Reply 3

black1blade

Don't just type everything into a calculator, write out all the numbers then simplify it by hand so to speak to get an exact answer. The one questions in core 2 you need a calculator for are trapezium rule questions.

Reply 4

username3538642

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(edited 6 years ago)

Reply 5

ManLike007

Original post by MathsAssist

The difference in how the solution was worked out lies in simplification of coefficients of x: I simplified the coefficients of x as far as possible (i.e. 8x^-5 + 3x^-1/2). The textbook solution on the other hand integrated the square roots directly, without converting into a more easily integrable form.

The integration method makes no difference itself because either way you'll get the same answer, (remember this is maths lol).

However, to get

-\frac{33}{8} +6 \sqrt 2

, don't express each surds to a few sig. figs for example. Keep everything in its form then simplify because there are some things a calculator won't simplify to an exact form and you'll have to do that by yourself.

(edited 6 years ago)

Reply 6

username3538642

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(edited 6 years ago)

Reply 7

black1blade

In pure maths unless doing something related to numerical methods we always put things into rationalized fractions.

Reply 8

black1blade

Original post by MathsAssist

This is the answer I needed. Thanks black1blade :biggrin:

What I did is I just stuck my formula into the calculator, and out came the answer.

Yeah don't do that unless you wanna lose half the marks.

Reply 9

Jarred

Never convert your answer into decimal unless explicitly asked. In general this means that if your answer has something like a fraction, a surd,

\pi

, or

e

then you should always leave your answer in terms of these rather than resolve it to a decimal. This is because of the precise reason you describe: it will often result in a loss of accuracy when punched into a calculator.

It might help to buy a calculator with a natural display as this will give some (but not all) answers in a pretty format. But most of the time you’ll be doing these calculations in your head anyway.