Maths with Lemon

Areas and Volumes

"In my free time I do differential and integral calculus. "

Karl Marx

Areas of Integrals

What you have to know:

Areas
(If not, check this lesson)
Recognize all the basic functions
How to integrate
(If not, check this lesson)
You must be able to manipulate logarithmic expressions.
(If not, check this lesson)

Areas

1. Watch the video:

2. Check out this presentation.

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

4. Read these notes.

Volumes 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.

Extra

Material and references:

Hodder Book HL(ISBN: 9781510462366) :
10I

Key Points

You should know that the area bounded by a curve \( x = g(y) \), the \( y \)-axis and the lines \( y = c \) and \( y = d \) is given by \[ \int_c^d g(y)\,dy. \]

You should know how to find volumes of revolution. The volume formed when the part of the curve \( y = f(x) \), between \( x = a \) and \( x = b \), is rotated about the \( x \)-axis is \[ V = \int_a^b \pi y^2\,dx. \] The volume formed when the part of the curve \( x = f(y) \), between \( y = c \) and \( y = d \), is rotated about the \( y \)-axis is \[ V = \int_c^d \pi x^2\,dy. \]

IB Past Paper Problems

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