Solving limits using integration.

Certain Limits can be evaluated by using a method known as limit as a sum. Transforming a limit question to integration makes it easy to solve. Sometimes, it is only possible way to solve a question. The method is explained in the image.

Note that above result is only true when limit is infinity. Also, integration not always go from 0 to 1. Again it depends on Limit. If summation is ending at 2x where x-> (infinity), integration is from 0 to 2. (Why so?). If you can't point out why, Mention in comments and I will answer.

However, lower limit is always zero given that summation starts from a finite value.

Since I don't know how to use Latex or how to insert image in middle of text, I am using image to explain it all. Can someone tell me how to write in Latex and insert images in between text.

#Calculus #Integration #Limts

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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Comments

"If summation is ending at 2x where x-> (infinity), integration is from 0 to 2." Please explain why and how? Can you please give one more example to eloborate it?

Uday Agrawal - 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$