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ali_dd

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Is the use of "without" in the following sentence correct grammatically and conceptually? If it is not , kindly suggest ways to make it clearer.

Figs. 15-19 are produced without using of integral.
 
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Tarheel

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Perhaps:

Figures 15 to 19 were produced without the use of integral __________.
 
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GoesStation

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Write without using an integral.
 
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Tarheel

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I looked up integral, and sure enough it can be used as a noun (in advanced mathematics).
 
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