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On a sketch of y=ln(x)y=ln(x), represent the left riemann sum with n=2n=2 approximating ∫65ln(x)dx∫56ln(x)dx. write out the terms of the sum, but do not evaluate it:

Respuesta :

W0lf93
Answer: y = f(x) = ln(x) sketch diagram , with 2 rectangles from the left side Sum = area of rectangle 1 + area of rectangle 2 = (1/2)(f(3)+f(3.5)) = ...plug values and calculator 2/ with 2 rectangles from the right side Sum = area of rectangle 1 + area of rectangle 2 = ...
isyllus

Answer:

[tex]\text{Left Riemann sum }= \frac{1}{2}(\ln 5+\ln 5.5)[/tex]

Step-by-step explanation:

We are given y=ln(x)

We need to represent the left riemann sum with n=2

Please see the attachment for sketch and two left rectangle.

[tex]I=\int_5^6 \ln xdx[/tex]

Left Riemann sum of integral

[tex]\int_a^bf(x)dx=\frac{b-a}{n}(f(x_0)+f(x_1))[/tex]

where, f(x)=ln(x), a=5 , b=6, n=2 , [tex]x_0=5[/tex] and [tex]x_1=5.5[/tex]

Now we write given integral into riemann sum

[tex]L_2=\frac{6-5}{2}(f(5)+f(5.5))[/tex]

[tex]L_2=\frac{1}{2}(\ln 5+\ln 5.5)\approx 1.6571[/tex]


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