Answer:
A.
Step-by-step explanation:
Answe
Given,
f(x) = 49 − x² from x = 1 to x = 7
n = 4
![\Delta x = \dfrac{7-1}{4}= 1.5](https://tex.z-dn.net/?f=%5CDelta%20x%20%3D%20%5Cdfrac%7B7-1%7D%7B4%7D%3D%201.5)
For x= 1
f(x₀) = 49 - 1^2 = 48
x = 2.5
f(x₁) = 42.75
x = 4
f(x₂) = 49 - 4^2 = 33
x = 5.5
f(x₃) = 49 - 5.5^2 = 18.75
x = 7
f(x₄) = 49 - 7^2 = 0
We have to evaluate the function on therigh hand point
![A = \Delta x [f(x_1)+f(x_2)+f(x_3)+f(x_4)]](https://tex.z-dn.net/?f=A%20%3D%20%5CDelta%20x%20%5Bf%28x_1%29%2Bf%28x_2%29%2Bf%28x_3%29%2Bf%28x_4%29%5D)
![A = 1.5 [42.75+33+18.75+0]](https://tex.z-dn.net/?f=A%20%3D%201.5%20%5B42.75%2B33%2B18.75%2B0%5D)
![A = 141.75](https://tex.z-dn.net/?f=A%20%3D%20141.75)
For Area for left hand sum
![A = \Delta x [f(x_0)+f(x_1)+f(x_2)+f(x_3)]](https://tex.z-dn.net/?f=A%20%3D%20%5CDelta%20x%20%5Bf%28x_0%29%2Bf%28x_1%29%2Bf%28x_2%29%2Bf%28x_3%29%5D)
![A = 1.5 [48+42.75+33+18.75]](https://tex.z-dn.net/?f=A%20%3D%201.5%20%5B48%2B42.75%2B33%2B18.75%5D)
![A =213.75](https://tex.z-dn.net/?f=A%20%3D213.75)
There is nothing there to work with
Answer:
We are given two points (0,0) and (8,15)
15-0/8-0= 15/8 --> 8/15 for tangent
y=8/15(x) + b
plug in point A
y= 8/15 (x) +3.6