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Maths HL Paper 1 Ques 8 Integration

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Leaving Cert

Higher Level – Integration

Question 8 Paper 1

By Cillian Fahy

and Darron Higgins

Integration Paper 1, Q8

Table of Contents:

  1. Basics
  2. Definite and Indefinite Integration
    1. Constant of Integration
    2. Definite Integrations
  3. Integration by Substitution
    1. Powers
    2. Exponential
    3. Rewriting
  4. Integration and Trigonometry
    1. Normal Trig. Functions
    2. Using Rules for Trig. Products
    3. Substitution for Trig. Functions
    4. Inverse Trig. Functions
  5. Area
    1. Curve and the x-axis
    2. Two curves or a curve and a line

Integration Basics:

We will begin our review of Integration with a quick overview of the basics. We will focus on clarifying the simple points which you may have overlooked. It’s important that you are certain on the simple steps as that can make the more difficult questions easier.


The basic rule of integration is: (Page 26, Table Book)

Meaning you take the power of X add 1 to it and then divide by that new power.

Question 1: How is Integration the reverse of differentiation? The basic idea behind integration is the following: When you differentiate y you get . When you integrate you get y.

You will find that all the rules below are very similar to Differentiation.

Question 2: What if I am asked to integrate with a number in front of it? You integrate as you usually would without the number and then multiply by that number.

In fact, we can do the following: where a is a constant (normal number).

Question 3: What if I am asked to integrate a number without an x? Just like in Differentiation, you think of a number without an x as a number multiplied by because Then just follow the formula above.

Question 4: What if I am asked to integrate two numbers added to each other? Again, just as in Differentiation, you integrate the terms separately and then add them together again.

Question 5: How do I deal with a Square root? You just look at the square root as and integrate normally then.

Question 6: How to I deal with an X below the line?

Think of what you would do for Differentiation. Just use indices...

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