Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Integration: ares under two curves

Did an exam recently with a question like the title says.

Used the ( integral of y1 - y2 ) dx rule, however, I integrated fully before working out y1 - y2. However, someone else smarter than me worked out y1-y2 before integrating.

Does that affect the overall answer or are the steps interchangeable?

Original post by Regret786

Did an exam recently with a question like the title says.

Used the ( integral of y1 - y2 ) dx rule, however, I integrated fully before working out y1 - y2. However, someone else smarter than me worked out y1-y2 before integrating.

Does that affect the overall answer or are the steps interchangeable?

Can you post an example of what you mean?

Integrating before subtracting is just taking the area under y₂ away from the area under y₁.

Subtracting before integrating gives you a different function, but the area under that curve is equivalent to the difference above.

In other words, yes, they're interchangeable.

I am curious too

OP

Original post by notnek

Can you post an example of what you mean?

Original post by TeeEm

I am curious too

http://qualifications.pearson.com/content/dam/pdf/International%20GCSE/Further%20Pure%20Mathematics/2009/Exam%20materials/Question-paper-Paper-2-June-2014.pdf

Question 7C. This isn't the exact question since the exam was on Fridays. The link is volume instead of curve.

Original post by Regret786

http://qualifications.pearson.com/content/dam/pdf/International%20GCSE/Further%20Pure%20Mathematics/2009/Exam%20materials/Question-paper-Paper-2-June-2014.pdf

Question 7C. This isn't the exact question since the exam was on Fridays. The link is volume instead of curve.

\displaystyle \int_a^b (y_1 - y_2)\mathrm{d}x = \int_a^b y_1 \mathrm{d}x - \int_a^b y_2 \, \mathrm{d}x

in general for continuous

y_1, y_2

.

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