Mathematics: 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:

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On a sketch of y=ln(x)y=ln(x), represent the left

NearNoodle23

14.03.2022

$\text{Left Riemann sum }= \frac{1}{2}(\ln 5+\ln 5.5)$

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.

$I=\int_5^6 \ln xdx$

Left Riemann sum of integral

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

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

Now we write given integral into riemann sum

$L_2=\frac{6-5}{2}(f(5)+f(5.5))$

$L_2=\frac{1}{2}(\ln 5+\ln 5.5)\approx 1.6571$

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