Compute the deﬁnite integral as the limit of Riemann sums.
-$$\int _ { b } ^ { C } a d x$$
A) $a ( c - b )$
B) $a$
C) $c - b$
D) $a \left( \frac { c ^ { 2 } } { 2 } - \frac { b ^ { 2 } } { 2 } \right)$

Question

Quizplus · Accepted Answer

Since the integrand is a constant function, each Riemann sum will be a rectangle with base width $c-b$ and height $a$. Therefore, the limit of the Riemann sums will be the area of a rectangle with base $c-b$ and height $a$, which is $a(c-b)$.

Compute the Deﬁnite Integral as the Limit of Riemann Sums ∫bCadx\int _ { b } ^ { C } a d x∫bC​adx

Compute the Deﬁnite Integral as the Limit of Riemann Sums $\int _ { b } ^ { C } a d x$