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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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Choose how you want to read, explain the wording that matters, and keep the book’s structure available in the downloaded EPUB.

  1. Choose your preferred English

    Use translation instructions to request British or American English and describe your preferred tone. For example: “Use British English and a clear, conversational tone.”

  2. Explain specialist terms and names

    Describe the book’s subject and provide preferred translations for important terms. You can also ask to keep personal names unchanged. Review recurring names and terminology in the finished book.

  3. Read English alone or compare languages

    Choose translation-only output for English text, or bilingual output with each original passage followed by its English translation. Use the original to check difficult or important passages.

  4. Keep chapters and navigation

    The result remains an EPUB, with chapters, the table of contents, images, and reading structure retained where possible. Check navigation and notes in your reader after downloading.

Frequently asked questions

Can I translate an entire book into English?

Yes. Upload the complete book as an EPUB and choose English as the target language. Check current upload and processing limits before submitting.

What is the difference between English-only and bilingual output?

Translation-only output contains the English translation. In a bilingual EPUB, each original passage is followed by its English translation so you can compare both languages while reading.

Can I request British or American English?

Write your preference in the translation instructions before submitting, for example: “Use British English.” Instructions guide the translation; check important wording in the finished book.

Where do I download the result and check the cost?

Download your EPUB from the completed task. New users receive trial credits, and translation is charged by usage. See Pricing for current rates.