Calculate 𝑅8 for𝑓(𝑥)=10−𝑥 over[ 3 , 5 ] .

Question

Calculate R8 for f(x)=10−x over [3,5]

R8= ??? (I keep getting 12 but is wrong also tried -12)

Calculate 𝐿4 for 𝑓(𝑥)=50cos(x^3) over [3𝜋/4,3𝜋/2]

L4= ???

Answer 1

··Δx = (5 - 3)/8 = 0.25; R₈ = ∑₁⁸(7 - 0.25i)·0.25 = 11.75.

Δx = (3π/2 - 3π/4)/4 = 3π/16; L₄ = ∑₀³50cos(3π/4 + 3πk/16)³(3π/16) = 97.8035

We use TI-84 sum(seq( function

Answer 2

I assume that R8 means use right endpoints with 8 equal subdivisions of the given interval?

If so, then Δx = (5-3)/8 = 0.25

The subdivision points are 3, 3.25, 3.5, 3.75, 4, 4.25, 4.5, 4.75, 5

R8 = f(3.25)(0.25)+(3.5)(0.25)+f(3.75)(0.25) + f(4)(0.25) + f(4.25)(0.25) + f(4.5)(0.25) + f(4.75)(0.25) +f(5)(0.25)

= 0.25[6.75 + 6.5 + 6.25 + 6 + 5.75 + 5.5 + 5.25 + 5] = 11.75