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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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From a book in another language to your next read

Translate the complete EPUB instead of copying passages into a text translator. Choose your language and output, then download a book you can keep reading.

  1. Translate the complete book

    Upload the EPUB as one file. PDF Craft processes the book so you can download the result without translating individual passages by hand.

  2. Keep chapters and reading structure

    Download a translated EPUB with chapters, the table of contents, images, and reading structure retained where possible. Open it in your reader and check navigation and notes against the original.

  3. Guide names, terms, and tone

    Use translation instructions to explain the subject and your preferred wording. For fiction, specify character names and tone. For nonfiction, describe the field and important terminology.

  4. Choose how you want to read

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Frequently asked questions

What book format should I upload?

This page is designed for EPUB books. Upload your EPUB, choose the target language, and select translated or bilingual output. For scanned PDF books, see PDF conversion.

Can I translate a book into English?

Yes. Choose English as the target language. See our EPUB-to-English page for the steps.

Can I translate a novel?

Yes. EPUB novels can use the same translation workflow. Add instructions for character names, recurring terms, and tone. See Novel Translator for a fiction-focused guide.