Midpoint rule with given value

9514 1404 393

  M₅ = 1.6570

Step-by-step explanation:

The basic idea is to find the function values at x ∈ {1.1, 1.3, 1.5, 1.7, 1.9}, add those values, and multiply the result by 1/5. Those x-values are the midpoints of intervals 0.2 units wide, between x = 1 and x = 2. The width 0.2 is the total interval width (2-1=1) divided by n = 5.

The calculation and results are shown in the attachment. Rounded to 4 decimal places, the integral is ...

  M₅ = 1.6570

__

The actual integral is about 1.6574, so this is pretty close.

three-fourths of an hour

36÷48=0.75

0.75=

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2