Maths with Lemon

Integration

"Every one who understands the subject will agree that even the basis on which the scientific explanation of nature rests is intelligible only to those who have learned at least the elements of the differential and integral calculus, as well as analytical geometry."

Felix Klein

Integration

What you have to know:

The derivatives of all known functions
(If not, check this lesson)
Recognize all the basic functions
You must be able to manipulate exponential expressions.
(If not, check this lesson)
You must be able to manipulate logarithmic expressions.
(If not, check this lesson)

Antidifferentiation / Integration

1. Watch the video:

2. Check out this presentation.

3. How to find the constant c. Check the example.

4. Read these notes.

Integration by substitution

What you have to know:

The derivatives of all known functions
(If not, check this lesson)

1. Watch the video:

2. Watch integrals by substitution with logs video.

3. Watch integrals by substitution with polynomial functions video.

Definite integrals

What you have to know:

The derivatives of all known functions
(If not, check this lesson)
Recognize all the basic functions
You must be able to manipulate exponential expressions.
(If not, check this lesson)
You must be able to manipulate logarithmic expressions.
(If not, check this lesson)

Key Points

1. Watch the video:

2. Watch this special case of definite integrals.

Areas of integrals

What you have to know:

The derivatives of all known functions
(If not, check this lesson)
Recognize all the basic functions
You must be able to manipulate exponential expressions.
(If not, check this lesson)
You must be able to manipulate logarithmic expressions.
(If not, check this lesson)

Key Points

1. Watch the video:

2. Watch this video to find areas using a calculator.

3. Watch this video.

IB Past Paper Problems

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