# Numbers | Maths with Lemon

Source: https://mathswithlemon.io/aa-calculus-areas-volumes.html


## 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 \[ V = \int_c^d \pi x^2\,dy. \]

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