question let f be the function defined by f(x)=3ln(x). if five subintervals of equal length are used, what…

question let f be the function defined by f(x)=3ln(x). if five subintervals of equal length are used, what is the value of the right riemann sum approximation for ∫233ln(x)dx? round to the nearest thousandth if necessary. answer attempt 2 out of 3 2.874 submit answer

question let f be the function defined by f(x)=3ln(x). if five subintervals of equal length are used, what is the value of the right riemann sum approximation for ∫233ln(x)dx? round to the nearest thousandth if necessary. answer attempt 2 out of 3 2.874 submit answer

Answer

Answer:

$2.874$

Explanation:

Step1: Calculate width of sub - intervals

$\Delta x=\frac{3 - 2}{5}=0.2$

Step2: Determine right - hand endpoints

$x_1 = 2.2,x_2=2.4,x_3 = 2.6,x_4=2.8,x_5 = 3$

Step3: Evaluate function at endpoints

$f(x_1)=3\ln(2.2),f(x_2)=3\ln(2.4),f(x_3)=3\ln(2.6),f(x_4)=3\ln(2.8),f(x_5)=3\ln(3)$

Step4: Calculate right Riemann sum

$R_5=\sum_{i = 1}^{5}f(x_i)\Delta x=0.2\times(3\ln(2.2)+3\ln(2.4)+3\ln(2.6)+3\ln(2.8)+3\ln(3))\approx2.874$