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Question Number 23432 by last updated on 30/Oct/17

∫_0 ^a f(x)dx=

$$\int_{\mathrm{0}} ^{{a}} {f}\left({x}\right){dx}= \\ $$

Answered by Joel577 last updated on 31/Oct/17

Let F(x) is an anti derivative of f(x)  I = ∫_0 ^a  f(x) dx = [F(x)]_0 ^a  = F(a) − F(0)

$$\mathrm{Let}\:{F}\left({x}\right)\:\mathrm{is}\:\mathrm{an}\:\mathrm{anti}\:\mathrm{derivative}\:\mathrm{of}\:{f}\left({x}\right) \\ $$$${I}\:=\:\underset{\mathrm{0}} {\overset{{a}} {\int}}\:{f}\left({x}\right)\:{dx}\:=\:\left[{F}\left({x}\right)\right]_{\mathrm{0}} ^{{a}} \:=\:{F}\left({a}\right)\:−\:{F}\left(\mathrm{0}\right) \\ $$

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