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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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Keep your Spanish EPUB in the PDF Craft library

After translating online, download the EPUB and open it in PDF Craft Desktop to read in Spanish and check passages against the source. Keep both editions in your local library, or open the translated file in your usual EPUB reader.

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Turn your EPUB into a Spanish reading edition

This workflow is for an EPUB you want to read in Spanish. Upload the complete file, choose Spanish in the language settings, select an output mode, and submit the task.

  1. Translate the book into Spanish

    Process the book as an EPUB rather than translating copied passages separately. Chapters, table of contents, and images are retained where possible; check the downloaded book in your reader.

  2. Read Spanish alone or beside the source

    Choose translation-only output for Spanish text in place of the original. Choose bilingual output to keep each source passage followed by its Spanish translation.

  3. Specify the Spanish you prefer

    Use the translation instructions field to state regional or tone preferences and preferred names. For example: “Use Spanish from Spain, an informal tone, and keep product names unchanged.” These are translation instructions, not a guarantee of uniform wording.

  4. Use trial credits and download when ready

    New users receive trial credits. Translation charges depend on usage and are deducted from your shared balance; see Pricing for current rates. Download the EPUB from the completed task and open it to start reading in Spanish.