Summary
Summary OCR MEI Mathematics: Year 2 Pure - Integration Cheat Sheet
- Course
- Institution
This document briefly summarises the key points in the Year 2 'Integration' topic of OCR's Mathematics (MEI) course.
[Show more]
1 review
By: tsmith3553 • 1 year ago
Seller
Follow
JodbyBerundi
Reviews received
Content preview
IntegrationFinding Areas
● Can find the area under a curve by integrating
● The same idea can be used to find the area between
a curve and the y-axis
● Instead of integrating with respect to x, we are
integrating with respect to y
● Therefore we use y-values as the limits and we must
express the expression to be integrated in terms of y
Area Between a Line and a Curve
● When finding the area between a line and a curve, we can subtract the
area underneath the curve from the area underneath the line
● Can integrate to find the area under the curve and can use the triangle
area formula to find the area under the line
● Can also integrate both expressions:
a
○ Area = ∫ (f (x) − g(x))
b
○ f (x) = equation of line, g (x) = equation of curve
● The above approach can also be used to find the area between two curves
Integration by Substitution
● Chain rule allows differentiation of a function of x by making a substitution
with another variable, u
● However, integration is not as easy - we are integrating with respect to x ,
not with respect to u
● Therefore we must change the dx in the equation to a du by multiplying by
du
dx
● This means we divide the function by the derivative of u and then proceed
as normal
● This can often make problems easier, as cancelling can occur
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller JodbyBerundi. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $3.90. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
75323 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now