Invoking deep thoughts: Integration

Why don't we add a constant of integration when integrating the second function while applying integration by parts? I'm searching for a perfectly logical answer

#Calculus #Integration

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

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}`	$\boxed{123}$

Comments

Thanks for asking this question, I had the same one in my mind!

Swapnil Das - 5 years, 11 months ago

Well I've reasoned something out... I'm waiting for some other replies

Mayank Singh - 5 years, 11 months ago

It will not affect the final answer. You can try it out yourself. The extra part, if you think there will be any, will get cancelled out at the end.

Sanchit Aggarwal - 5 years, 11 months ago

What if I took different constants while integrating

P.S. You have to integrate g(x) twice while applying by parts

Mayank Singh - 5 years, 11 months ago

Ofcourse you cannot take different constants. You are integrating only one function, no matter twice. It should be the same general constt., or no constant at all.

P.s. refer to the derivation of the formula once

Sanchit Aggarwal - 5 years, 11 months ago

What is "the second function"? On $\int u \, dv = uv - \int v \, du$ , is the second function $v$ or $v \, du$ ?

Ivan Koswara - 5 years, 11 months ago

The second function is 'dv', the function whose integral is 'v'

Sanchit Aggarwal - 5 years, 11 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}`	$\boxed{123}$