<div class="text-justify"> ![image.png](https://images.hive.blog/DQmTjMvd5MBSUsS5wj19dyoPGYUW4zovvUyJvVAgZd2F7U7/image.png) [Fuente de imagen](https://commons.wikimedia.org/wiki/File:Riemann_sum_convergence.png) Hola amigos de la comunidad científica y académica de la blockchain. Quizás muchos estudiantes que se inician en el mundo universitario en el área de ciencia e ingeniería han escudriñado un libro de cálculo y hayan leído que una integral es una antiderivada. Por lo que resulta necesario asumir que si una integral es una antiderivada, podemos decir en lugar de integral decir antiderivada, o en vez de decir antiderivada decir integral, ya que dentro del cálculo integral son términos conceptuales que terminan siendo sinónimos. El objetivo de este post es analizar el concepto de integral y demostrar con algunos ejemplos por qué una integral puede ser llamada antiderivada. ### ***¿Qué es una integral?*** <p> Una integral es una simbología para expresar esa capacidad existente de poder sumar infinitesimalmente pequeños pedazos de trozos de área de una región, o en su defecto también se define analíticamente como la operación inversa a la derivada de una función (diferenciación). ![image.png](https://images.hive.blog/DQmbYyCVnp6WyPjQdu9SJNbb7cgnvkY6MECgMRCSH6cjXjm/image.png) [Fuente de imagen](https://commons.wikimedia.org/wiki/File:Integral_example.png) Si partimos de la idea analítica de que una integral es una antiderivada es porque una integral es lo que conseguimos como resultado que esta antes del resultado de una derivada, por lo que es común también encontrar en los textos el concepto de integral como una primitiva, ya que realmente lo que conseguimos cuando integramos es la función original de la derivada. Para entender un poco mejor este concepto de integral, antiderivada o primitiva, vamos a partir de proporcionar la siguiente función real: ![image.png](https://images.hive.blog/DQmb6ZFgAbrLuxdmoXKEsgvKoCJPaszHoWb1zs4UkdESWqC/image.png) <center><sup>autor de la imagen: @carlos84</sup></center> A esta función le vamos a encontrar la derivada: ![image.png](https://images.hive.blog/DQmPgrk9pJkncmqznjD1ovFUi3TaCfJrTxPYvFSSKvLmvHs/image.png) <center><sup>autor de la imagen: @carlos84</sup></center> Como pueden observar ya encontramos la derivada de la función polinómica, por lo que de ser cierto lo del concepto de lo que una integral es una antiderivada, entonces vamos a integrar el resultado de la derivada y nos debería de dar la función original. ![image.png](https://images.hive.blog/DQmRFp4FrzjUXqmr38iJw4oyobHJpkXMtfPmfxFPvpqUWM9/image.png) <center><sup>autor de la imagen: @carlos84</sup></center> ![image.png](https://images.hive.blog/DQmczjJnTn8aESdEekn5m8MMv4c8j1oe8XiKAwx2mxXJUpe/image.png) <center><sup>autor de la imagen: @carlos84</sup></center> Como pueden observar en la imagen anterior el resultado de resolver la integral propuesta es el mismo resultado de la función polinómica original, sin embargo el tercer término que es el número 5 se ve reflejado en la constante de integración (c). Por lo tanto podemos llegar a la conclusión que ciertamente una integral es una antiderivada o primitiva. ### ***Bibliografía consultada y recomendada*** <p> - Libro de Cáculo con Geometría analitica de Larson y Hostetler - Libro de Cáculo con Geometría analitica de Leithold. 7ma edición </div>
author | carlos84 |
---|---|
permlink | por-que-el-sinonimo-de-una-integral-es-antiderivada |
category | hive-196387 |
json_metadata | {"tags":["spanish","piotr","stem-espanol","cervantes","ciencia","stem","neoxian"],"users":["carlos84"],"image":["https://images.hive.blog/DQmTjMvd5MBSUsS5wj19dyoPGYUW4zovvUyJvVAgZd2F7U7/image.png","https://images.hive.blog/DQmbYyCVnp6WyPjQdu9SJNbb7cgnvkY6MECgMRCSH6cjXjm/image.png","https://images.hive.blog/DQmb6ZFgAbrLuxdmoXKEsgvKoCJPaszHoWb1zs4UkdESWqC/image.png","https://images.hive.blog/DQmPgrk9pJkncmqznjD1ovFUi3TaCfJrTxPYvFSSKvLmvHs/image.png","https://images.hive.blog/DQmRFp4FrzjUXqmr38iJw4oyobHJpkXMtfPmfxFPvpqUWM9/image.png","https://images.hive.blog/DQmczjJnTn8aESdEekn5m8MMv4c8j1oe8XiKAwx2mxXJUpe/image.png"],"links":["https://commons.wikimedia.org/wiki/File:Riemann_sum_convergence.png"],"app":"hiveblog/0.1","format":"markdown"} |
created | 2021-10-01 21:42:06 |
last_update | 2021-10-01 21:42:06 |
depth | 0 |
children | 4 |
last_payout | 2021-10-08 21:42:06 |
cashout_time | 1969-12-31 23:59:59 |
total_payout_value | 12.034 HBD |
curator_payout_value | 11.927 HBD |
pending_payout_value | 0.000 HBD |
promoted | 0.000 HBD |
body_length | 3,385 |
author_reputation | 353,218,698,404,153 |
root_title | "¿Por qué el sinónimo de una integral es antiderivada?" |
beneficiaries | [] |
max_accepted_payout | 1,000,000.000 HBD |
percent_hbd | 10,000 |
post_id | 106,708,486 |
net_rshares | 18,606,339,662,189 |
author_curate_reward | "" |
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technologix | 0 | 577,515,536 | 0.9% | ||
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motherofalegend | 0 | 1,122,502,580 | 5% | ||
truthtrader | 0 | 1,030,448,012 | 25.5% | ||
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juanmolina | 0 | 79,058,064,667 | 60% | ||
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deathcross | 0 | 46,744,902,906 | 100% | ||
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lupafilotaxia | 0 | 888,163,265,543 | 60% | ||
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steemitcentral | 0 | 171,137,250,474 | 70% | ||
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drricksanchez | 0 | 10,564,166,687 | 2.5% | ||
genx-miner | 0 | 2,951,277,363 | 100% | ||
counterterrorism | 0 | 439,923,137 | 0.45% | ||
cristanza42 | 0 | 35,842,171,242 | 60% | ||
sidalim88 | 0 | 46,220,040,999 | 60% |
Hola @carlos84 ilustrativo y claro el ejemplo que tomas en tu post.
author | alfonsoalfonsi |
---|---|
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Hola amigo @alfonsoalfonsi. Gracias por leer y comentar, saludos.
author | carlos84 |
---|---|
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Electronic-terrorism, voice to skull and neuro monitoring on Hive and Steem. You can ignore this, but your going to wish you didnt soon. This is happening whether you believe it or not. https://ecency.com/fyrstikken/@fairandbalanced/i-am-the-only-motherfucker-on-the-internet-pointing-to-a-direct-source-for-voice-to-skull-electronic-terrorism
author | gangstalking |
---|---|
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<div class='text-justify'> <div class='pull-left'> <img src='https://stem.openhive.network/images/stemsocialsupport7.png'> </div> Thanks for your contribution to the STEMsocial community. Feel free to join us on discord to get to know the rest of us! Please consider <a href="https://hivesigner.com/sign/update-proposal-votes?proposal_ids=%5B91%5D&approve=true">supporting our funding proposal</a>, <a href="https://hivesigner.com/sign/account_witness_vote?approve=1&witness=stem.witness">approving our witness</a> (@stem.witness) or delegating to the @stemsocial account (for some ROI). Please consider using the <a href='https://stem.openhive.network'>STEMsocial app</a> app and including @stemsocial as a beneficiary to get a stronger support. <br /> <br />
author | steemstem |
---|---|
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