Compute the average of the RRAM and LRAM approximations to estimate the area between the graph of the function
and the x-axis over the given interval using the indicated number of subintervals. (The function is non-negative on the
given interval).
-$f ( x ) = 3 x + 3 ; [ 0,5 ] ; 5$ subintervals
A) $\frac { 123 } { 2 }$
B) $\frac { 105 } { 2 }$
C) $\frac { 87 } { 2 }$
D) 105

Question

Quizplus · Accepted Answer

The RRAM (Right Riemann Approximation Method) and LRAM (Left Riemann Approximation Method) are calculated using the endpoints of the subintervals. For $f(x) = 3x + 3$ over $[0,5]$ with 5 subintervals, the width of each subinterval is 1. The LRAM uses points $x = 0, 1, 2, 3, 4$ and the RRAM uses points $x = 1, 2, 3, 4, 5$. Calculating both and averaging gives $\frac{105}{2}$.

Compute the Average of the RRAM and LRAM Approximations to Estimate