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08.01.2023 05:43
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If f(x) = 5x2 − 2x, 0 ≤ x ≤ 3, evaluate the riemann sum with n = 6, taking the sample

If f(x) = 5x2 − 2x, 0 ≤ x ≤ 3, evaluate the riemann sum with n = 6, taking the sample points to be right endpoints. r6 =
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melanie12566
melanie12566
4,9(84 marks)

46.375

Step-by-step explanation:

Given information:

f(x)=5x^2-2x

where, 0 ≤ x ≤ 3.

We need to divde the interval [0,3] in 6 equal parts.

The length of each sub interval is

\dfrac{b-a}{n}=\dfrac{3-0}{6}=0.5

Right end points are 0.5, 1, 1.5, 2, 2.5, 3.

The value function on each right end point are

f(0.5)=5(0.5)^2-2(0.5)=0.25

f(1)=5(1)^2-2(1)=3

f(1.5)=5(1.5)^2-2(1.5)=8.25

f(2)=5(2)^2-2(2)=16

f(2.5)=5(2.5)^2-2(2.5)=26.25

f(3)=5(3)^2-2(3)=39

Riemann sum:

\sum_{n=1}^6 f(x_n)\Delta x_n

Sum=[f(0.5)+f(1)+f(1.5)+f(2)+f(2.5)+f(3)]\times 0.5

Sum=[0.25+3+8.25+16+26.25+39]\times 0.5

Sum=92.75\times 0.5

Sum=46.375

Therefore, the Riemann sum with n = 6 is 46.375.

memelord4206969
memelord4206969
4,6(70 marks)

Step-by-step explanation:

I dont even know

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