Question

Question attached as screenshot belowPlease help me I am following alongI want to be better at maths

Answer 1

Step 1:

write the function

`f(x)=x^2\text{ + 1}`

Step 2

split the range in three identical invervals of size

`\begin{gathered} =\text{ }\frac{6\text{ - 0}}{3} \\ =\text{ 2} \end{gathered}`

Step 3:

For the first rectangle , base = 2

`\begin{gathered} \text{Height = 2}^2\text{ + 1 = 4 + 1 = 5} \\ \text{Area = base }*\text{ Height = 2 }*\text{ 5 = 10} \end{gathered}`

Step 4:

For the second area

Base = 2

`\begin{gathered} \text{Height is f(2+2) = f(4) = 4}^2\text{ + 1 = 16 + 1 = 17} \\ \text{Area = 2 }*\text{ 17 = 34} \end{gathered}`

Step 5:

For the the third rectangle

Base = 2

`\begin{gathered} \text{Height is f(4 + 2) = }6^2\text{ + 1 = 36 + 1 = 37} \\ \text{Area = 2 }*\text{ 37 = 74} \end{gathered}`

Total area = 10 + 34 + 74 = 118

Area under the curve = 118