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Original · English

Calculus Made Easy

Chapter I

A little bit of. The sum of.

These dreadful symbols are:

(1) d which merely means “a little bit of.” Thus dx means a little bit of x; or du means a little bit of u. But you will find that these little bits (or elements) may be considered to be indefinitely small.

dx,du

(2) ∫ which is merely a long S, and may be called (if you like) “the sum of.” Thus ∫dx means the sum of all the little bits of x; or ∫dt means the sum of all the little bits of t.

∫dx,∫dt

The word “integral” simply means “the whole.” If you think of the duration of time for one hour, you may (if you like) think of it as cut up into 3600 little bits called seconds. The whole of the 3600 little bits added up together make one hour.

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Translation · European Spanish

El cálculo al alcance de todos

Capítulo I

Un poquito. La suma.

Estos temibles símbolos son:

(1) d, que solo significa «un poquito de». Así, dx es un poquito de x; du, un poquito de u. Pero verá que estos pequeños trozos (o elementos) pueden considerarse indefinidamente pequeños.

dx,du

(2) ∫, que no es más que una S alargada y puede llamarse, si lo desea, «la suma de». Así, ∫dx es la suma de todos los pequeños trozos de x; ∫dt, la de todos los de t.

∫dx,∫dt

La palabra «integral» significa simplemente «el todo». Puede imaginar una hora dividida en 3600 pequeños trozos llamados segundos. Todos esos 3600 trozos sumados forman una hora.

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Start with the EPUB file you already have. Sign in when prompted, upload the book, choose the target language and output mode, then submit the task.

  1. Upload the book as one EPUB file

    Submit the complete EPUB rather than copying chapters into a text translator. The result stays in EPUB format, with chapters, navigation, and images retained where possible.

  2. Choose translation-only or bilingual output

    A translation-only EPUB replaces the source text. A bilingual EPUB keeps each original passage followed by its translation, so you can compare the two while reading.

  3. Explain the translation you need

    Before submitting, add any useful background, preferred names, terminology, or tone in the translation instructions field. For example: “This is a history book; keep place names in their original form.”

  4. Check pricing and download the result

    New-user trial credits are available, and translation is billed by usage from your shared balance. See Pricing for current rates. When processing completes, download the EPUB from the task and open it in your reader.