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Intergration

I am trying to understand how integration works. I checked text books but they don't offer the basics. For example what process would you need to integrate y=x, is it integration by parts?

Reply 1

shawtyb

Integration is the inverse process to differentiation. So instead of multiplying by the index and reducing the index by one, we increase the index by one and divide by the new index. For example, becomes . The appears because the derivative of any constant term is zero.

Reply 2

Zacken

Original post by cosv

I am trying to understand how integration works. I checked text books but they don't offer the basics. For example what process would you need to integrate y=x, is it integration by parts?

Differentiation is finding the gradient of a curve. Integration is finding the area between a curve. It is defined as the limit of riemann sums (for definite integrals). That is, make a bunch of rectangles to estimate the area of the graph, then send the width of each rectangle in the limit to 0 and sum them all up. One short cut in integration is:

Unparseable latex formula:

\displaystyle \begin{equation*} \int x^n \, \mathrm{d}x = \frac{x^{n+1}}{n+1} + \mathcal{C} \end{equation*}

for

n \neq -1

(edited 8 years ago)

Reply 3

TeeEm

Original post by cosv

I am trying to understand how integration works. I checked text books but they don't offer the basics. For example what process would you need to integrate y=x, is it integration by parts?

what is your mathematics level please?

Reply 4

TeeEm

Original post by Zacken

. It is defined as the limit of riemann sums.

Reply 5

Zacken

Original post by TeeEm

Reply 6

Gregorius

Original post by Zacken

It is defined as the limit of riemann sums (for definite integrals).

Henri Lebesgue est à la recherche pour vous. Il est très en colère.

Reply 7

Zacken

Original post by Gregorius

Henri Lebesgue est à la recherche pour vous. Il est très en colère.

Les mesures? C'est une beauté.

Reply 8

atsruser

Original post by Gregorius

Henri Lebesgue est à la recherche pour vous. Il est très en colère.

Et les nazis de la grammaire sont à la recherche de vous aussi, mon ami. Vous pouvez toujours courir, mais vous ne pouvez pas vous cacher!!!!

Reply 9

Gome44

je suis une pomme de terre

Reply 10

Gregorius

Original post by atsruser

Et les nazis de la grammaire sont à la recherche de vous aussi, mon ami. Vous pouvez toujours courir, mais vous ne pouvez pas vous cacher!!!!

Teach me for trying to be clever. Distressed to see that the powers that be are trying to get rid of the circumflex. Is nothing sacred?

Reply 11

atsruser

Original post by Gregorius

Teach me for trying to be clever. Distressed to see that the powers that be are trying to get rid of the circumflex. Is nothing sacred?

Don't worry - I've probably made a mistake somewhere too. Still, I can see that when it comes to modern developments in the French language, you clearly know your ognons.

But however are French people going to indicate exponentiation now? - that's what really worries me.