Integration

Question 1

What is integration?

Answer 1

The opposite of differentiation

Question 2

When would Integration be used?

Answer 2

Finding the area between a curve and the x axis between two points

Question 3

What is the notation for integration?

Answer 3

Question 4

What is the difference between indefinite and definite integration?

Answer 4

Indefinite means we don’t have x values to take into account, so there will always be + c at the end, as the exact expression is unknown

Question 5

What are the steps for integration?

Answer 5

1. Increase the power by 1
2. Divide the coefficient by this NEW power
3. If indefinite integration then add + c at the end

Question 6

What are the general integration formula’s ?

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Question 8

What is a way to check integration?

Answer 8

If differentiated gives the original answer

Question 9

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Question 11

General tips to remember when integrating:

Answer 11

1. Always remembering the + c
2. When expanding/ manipulating the original expression keep it in brackets with the dx
3. Look at what they want you to integrate with respect to (dx or dn or dp)

Question 12

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Question 13

What is the constant of integration?

Answer 13

The + c that comes at the end of indefinite integration

Question 14

What are the two phrases in which you will be required to find the constant of integration?

Answer 14

1. Given the gradient function to integrate and a point on the curve
2. Given a second derivative to integrate and a gradient at at given point

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Question 18

What is the notation of definite integrals?

Answer 18

Question 19

What is the difference between a definite integral and an indefinite integral ?

Answer 19

A definite integral produces a value.
An indefinite integral produces a function

Question 20

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Question 24

What information is needed to find the area under the curve?

Answer 24

1. The equation of the curve
2. The limits at the the area starts and ends
3. (Optional ) sketch is preferred

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Question 30

What is the quick method for finding the area between two curves ?

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Question 32

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