Maths - Integration by Substitution
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Flashcards
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\[\int (x+2)^5 dx\]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 $dx$?
\[du\]
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\[\int (x+2)^5 dx\]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?
\[[4, 16]\]
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\[\int \sqrt{1 + x^2}\]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??
\[u = 2\sinh x\]2022-04-12
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\[\int \frac{1}{2} x^3 \sqrt[3]{4 - x^2} \text{d}x\]What substitution should you make here??
\[u = 4 - x^2\]