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if-a-b-f-x-dx-7-and-a-b-4-g-x-dx-6-find-a-b-3-f-x-8-g-x-dx-




Question Number 146744 by mathdanisur last updated on 15/Jul/21
if  ∫_a ^b f(x)dx = 7   and  ∫_a ^b 4 g(x)dx = −6  find   ∫_a ^b (3 f(x)−8 g(x)) dx = ?
$${if}\:\:\underset{\boldsymbol{{a}}} {\overset{\boldsymbol{{b}}} {\int}}{f}\left({x}\right){dx}\:=\:\mathrm{7}\:\:\:{and}\:\:\underset{\boldsymbol{{a}}} {\overset{\boldsymbol{{b}}} {\int}}\mathrm{4}\:{g}\left({x}\right){dx}\:=\:−\mathrm{6} \\ $$$${find}\:\:\:\underset{\boldsymbol{{a}}} {\overset{\boldsymbol{{b}}} {\int}}\left(\mathrm{3}\:{f}\left({x}\right)−\mathrm{8}\:{g}\left({x}\right)\right)\:{dx}\:=\:? \\ $$
Answered by liberty last updated on 15/Jul/21
⇒3×7−2(−6)=21+12=33
$$\Rightarrow\mathrm{3}×\mathrm{7}−\mathrm{2}\left(−\mathrm{6}\right)=\mathrm{21}+\mathrm{12}=\mathrm{33} \\ $$
Commented by mathdanisur last updated on 15/Jul/21
thanks Ser
$${thanks}\:{Ser} \\ $$

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