Calculate the Riemann Sum for the integral using n = 5.
$\int _ { 0 } ^ { 1 } \frac { 3 } { 4 + x } d x$ ?
Give the answer correct to two decimal places.

A)0.33
B) 0.81
C) 0.68
D) 0.65
E) 0.53

Question

Calculate the Riemann Sum for the integral using n = 5.  
 $\int _ { 0 } ^ { 1 } \frac { 3 } { 4 + x } d x$ ?
Give the answer correct to two decimal places.
 
A)0.33
B) 0.81
C) 0.68
D) 0.65
E) 0.53

Quizplus · Accepted Answer

To calculate the Riemann Sum for the given integral $\int _ { 0 } ^ { 1 } \frac { 3 } { 4 + x } d x$ using $n = 5$, we first divide the interval [0, 1] into 5 equal parts, each of width $\Delta x = \frac{1-0}{5} = 0.2$. Then, for each subinterval, we evaluate the function at the right endpoint and multiply by $\Delta x$. Summing these values gives the Riemann Sum approximation for the integral.The right endpoints are $0.2, 0.4, 0.6, 0.8, $ and $1.0$. Evaluating the function at these points and summing gives:$\sum_{i=1}^{5} \frac{3}{4 + x_i} \Delta x = \frac{3}{4 + 0.2}(0.2) + \frac{3}{4 + 0.4}(0.2) + \frac{3}{4 + 0.6}(0.2) + \frac{3}{4 + 0.8}(0.2) + \frac{3}{4 + 1.0}(0.2)$Calculating each term and summing gives approximately 0.68, hence the correct answer is C.

Calculate the Riemann Sum for the Integral Using N = ∫0134+xdx\int _ { 0 } ^ { 1 } \frac { 3 } { 4 + x } d x∫01​4+x3​dx

Calculate the Riemann Sum for the Integral Using N = $\int _ { 0 } ^ { 1 } \frac { 3 } { 4 + x } d x$