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Change of Variable Formula
If:
$$x=\phi(t)$$
then:
$$\int_a^b f(x)\,dx=\int_{\alpha}^{\beta}f(\phi(t))\phi'(t)\,dt$$
where:
$$\phi(\alpha)=a,\quad\phi(\beta)=b$$
Usage
- Used to transform a definite integral into a more convenient variable.
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Change of Variable Formula
If:
$$x=\phi(t)$$
then:
$$\int_a^b f(x)\,dx=\int_{\alpha}^{\beta}f(\phi(t))\phi'(t)\,dt$$
where:
$$\phi(\alpha)=a,\quad\phi(\beta)=b$$
Usage
- Used to transform a definite integral into a more convenient variable.
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