Express the Limit as a Definite Integral $\lim_{{||P|| \rightarrow 0}} \sum_{\mathrm{k}=1}^{\mathrm{n}}\left(\sin \mathrm{c}_{\mathrm{k}}\right) \Delta \mathrm{x}_{\mathrm{k}}$

question 32

Multiple Choice

Express the limit as a definite integral.

- $\lim_{{||P|| \rightarrow 0}} \sum_{\mathrm{k}=1}^{\mathrm{n}}\left(\sin \mathrm{c}_{\mathrm{k}}\right) \Delta \mathrm{x}_{\mathrm{k}}$ , where $\mathrm { P }$ is a partition of $[ - \pi / 4,0 ]$

• A) \(\int _ { 1 } ^ { n } \sin x d x\)
• B) \(\int _ { - \pi / 4 } ^ { 0 } \cos x d x\)
• C) \(\int _ { 0 } ^ { \pi / 4 } \sin x d x\)
• D) \(\int _ { - \pi / 4 } ^ { 0 } \sin x d x\)

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