Integral with Both Limits as Functions

Rarely Tested

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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