Integral with Both Limits as Functions
If:
$$F(x)=\int_{g(x)}^{h(x)}f(t)\,dt$$
then:
$$F'(x)=f(h(x))h'(x)-f(g(x))g'(x)$$
Usage
- Used to differentiate integrals whose upper and lower limits both depend on $$x$$.
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CAT Formulas
Indefinite Integration
Integral with Both Limits as Functions
Integral with Both Limits as Functions
If:
$$F(x)=\int_{g(x)}^{h(x)}f(t)\,dt$$
then:
$$F'(x)=f(h(x))h'(x)-f(g(x))g'(x)$$
Usage
- Used to differentiate integrals whose upper and lower limits both depend on $$x$$.
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