Free Riemann sums with sigma notation Practice Problems • Learn To Be

The following graph shows a Riemann sum:

Which of the following approximates the area between $f(x)$ and the $x$ -axis on the interval $\left[0,\dfrac{1}{3}\pi \right]$ using a midpoint Riemann sum with $6$ equal subdivisions?

Choose 1 answer:

A
$\displaystyle {\sum_{i=0}^{6}} { \tan \left( \dfrac{\pi}{36}+{\dfrac{\pi}{18}}i \right) } \cdot {\dfrac{\pi}{6}}$
B
$\displaystyle {\sum_{i=0}^{5}} { \tan \left( \dfrac{\pi}{36}+{\dfrac{\pi}{18}}i \right) } \cdot {\dfrac{\pi}{6}}$
C
$\displaystyle {\sum_{i=0}^{5}} { \tan \left( \dfrac{\pi}{36}+{\dfrac{\pi}{18}}i \right) } \cdot {\dfrac{\pi}{18}}$
D
$\displaystyle {\sum_{i=0}^{6}} { \tan \left( \dfrac{\pi}{36}+{\dfrac{\pi}{18}}i \right) } \cdot {\dfrac{\pi}{18}}$

Riemann sums with sigma notation

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