Question

f(x) = 49 − x2 from x = 1 to x = 7; 4 subintervals

Answer 1

Answe

Given,

f(x) = 49 − x² from x = 1 to x = 7

n = 4

$\Delta x = \dfrac{7-1}{4}= 1.5$

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

$A = \Delta x [f(x_1)+f(x_2)+f(x_3)+f(x_4)]$

$A = 1.5 [42.75+33+18.75+0]$

$A = 141.75$

For Area for left hand sum

$A = \Delta x [f(x_0)+f(x_1)+f(x_2)+f(x_3)]$

$A = 1.5 [48+42.75+33+18.75]$

$A =213.75$