Question

Express the area A of the triangle as a function of x. a(x)=

Answer 1

..

Given:

`y=x^2`

The area of the right angle triangle is

`A_{\text{triangle}}=(1)/(2)* width* height`

From the right triangle in the curve given, the dimension of the width and height is

`\begin{gathered} width=x \\ height=y \end{gathered}`

Therefore, the area becomes

`A_{\text{triangle}}=(1)/(2)* x* y`
`\begin{gathered} \text{Note} \\ y=x^2 \\ \text{Therefore,} \\ A_{\text{triangle}}=(1)/(2)* x* x^2 \\ A_{\text{triangle}}=(1)/(2)* x^3 \end{gathered}`

Hence:

A(x) = x³/2