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Question Number 58627 by rahul 19 last updated on 26/Apr/19

Commented by rahul 19 last updated on 26/Apr/19

Ans: a,b,c

$${Ans}:\:{a},{b},{c} \\ $$

Commented by tanmay last updated on 26/Apr/19

pls mention the inerval of x for f(x) and g(x)

$${pls}\:{mention}\:{the}\:{inerval}\:{of}\:{x}\:{for}\:{f}\left({x}\right)\:{and}\:{g}\left({x}\right) \\ $$$$ \\ $$

Commented by rahul 19 last updated on 26/Apr/19

Sir, i have provided the complete Q.

$${Sir},\:{i}\:{have}\:{provided}\:\:{the}\:{complete}\:{Q}. \\ $$

Answered by tanmay last updated on 27/Apr/19

f(x)=3x^2 −2x+1 f(∣x∣)=3∣x∣^2 −2∣x∣+1 given x<−1 so ∣x∣=−x −∣x∣=x f(−∣x∣)=3x^2 −2x+1=2x^2 +(x−1)^2 g(x)=2x^2 +(x−1)^2 from attached curve of g(x) it is clear that a,b and d not true. ∫_(−4) ^(−2) 3x^2 −2x+1 dx =∣((3x^3 )/3)−((2x^2 )/2)+x∣_(−4) ^(−2) ={(−2)^3 −(−2)^2 +(−2)}−{(−4)^3 −(−4)^2 +(−4)} =(−8−4−2)−(−64−16−4) =−14+84=70

$${f}\left({x}\right)=\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1} \\ $$$${f}\left(\mid{x}\mid\right)=\mathrm{3}\mid{x}\mid^{\mathrm{2}} −\mathrm{2}\mid{x}\mid+\mathrm{1} \\ $$$${given}\:{x}<−\mathrm{1}\:\:{so}\:\mid{x}\mid=−{x} \\ $$$$−\mid{x}\mid={x} \\ $$$${f}\left(−\mid{x}\mid\right)=\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}=\mathrm{2}{x}^{\mathrm{2}} +\left({x}−\mathrm{1}\right)^{\mathrm{2}} \\ $$$${g}\left({x}\right)=\mathrm{2}{x}^{\mathrm{2}} +\left({x}−\mathrm{1}\right)^{\mathrm{2}} \\ $$$${from}\:{attached}\:{curve}\:{of}\:{g}\left({x}\right)\:{it}\:{is}\:{clear}\:{that} \\ $$$${a},{b}\:{and}\:{d}\:{not}\:{true}.\: \\ $$$$\int_{−\mathrm{4}} ^{−\mathrm{2}} \mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}\:\:{dx} \\ $$$$=\mid\frac{\mathrm{3}{x}^{\mathrm{3}} }{\mathrm{3}}−\frac{\mathrm{2}{x}^{\mathrm{2}} }{\mathrm{2}}+{x}\mid_{−\mathrm{4}} ^{−\mathrm{2}} \\ $$$$=\left\{\left(−\mathrm{2}\right)^{\mathrm{3}} −\left(−\mathrm{2}\right)^{\mathrm{2}} +\left(−\mathrm{2}\right)\right\}−\left\{\left(−\mathrm{4}\right)^{\mathrm{3}} −\left(−\mathrm{4}\right)^{\mathrm{2}} +\left(−\mathrm{4}\right)\right\} \\ $$$$=\left(−\mathrm{8}−\mathrm{4}−\mathrm{2}\right)−\left(−\mathrm{64}−\mathrm{16}−\mathrm{4}\right) \\ $$$$=−\mathrm{14}+\mathrm{84}=\mathrm{70} \\ $$

Commented by tanmay last updated on 27/Apr/19

Commented by rahul 19 last updated on 28/Apr/19

thank u sir.

$${thank}\:{u}\:{sir}. \\ $$

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