Question

Estimate the area under f(x)=x^ 2 [0,2] using right endpoint approximation given n = 4

Answer 1

The given curve is

`f(x)=x^2`

To find the area under the curve we will use the integration

`A=\int_0^2x^2dx`
`\begin{gathered} A=[(x^(2+1))/(2+1)]_0^2 \\ \end{gathered}`

Simplify it

`A=[(x^3)/(3)]_0^2`

Substitute x by 2 and 0

`\begin{gathered} A=[(2^3)/(3)]-[(0^3)/(3)] \\ \\ A=(8)/(3)-(0)/(3) \\ \\ A=(8)/(3) \end{gathered}`

The area under the curve is 8/3 square units

The answer is A