See Also
Flashcards
$$\int (x+2)^5 dx$$ What subsitution could you make in terms of $u$??
$$ u = x + 2 $$
If $u = x + 2$, what is $\frac{du}{dx}$??
$$ \frac{du}{dx} = 1 $$
If $u = x + 2$ and $\frac{du}{dx} = 1$, what is $dx$??
$$ du $$
$$\int (x+2)^5 dx$$ If $u = x+2$ and $du = dx$, how could you rewrite the integral??
$$ \int u^5 du $$
$$\int u^5 du$$ What is this equal to??
$$ \frac{u^6}{6} + c $$
$$\frac{u^6}{6} + c$$ Can you reverse the subsitution $u = x + 2$??
$$ \frac{(x + 2)^6}{6} + c $$
2021-03-30
If the subsitution for an integral is $u = x^2$ and the bounds are $[2, 4]$, what are the new bounds??
$$ [4, 16] $$
$$\int \sqrt{1 + x^2}$$ What subsitution would you make??
$$ u = \sinh x $$
$$\int \sqrt{1 - x^2}$$ What subsitution would you make??
$$ u = \sin x $$
or
$$ u = \cos x $$
$$\int \sqrt{x^2 - 1}$$ What subsitution would you make??
$$ u = \cosh x $$
$$\int \sqrt{4 + 4^2}$$ What subsitution would you make??
$$ u = 2\sinh x $$
Backlinks
- [[Maths - Integration by Parts]]S
- [[Further Maths - Improper Integrals]]S
- [[Maths - Syllabus]]S
- [[Further Maths - Mean Value of a Function]]S
Metadata
date: 2021-03-29 10:15
tags:
- '@?maths'
- '@?further-maths'
- '@?integration'
- '@?school'
- '@?public'
title: Maths - Integration by Substitution