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Question Number 94135 by redmiiuser last updated on 17/May/20

$$f\left(x\right)isacontinuousfunctionforallrealvaluesofxandsatisfies{\int }_0^{x}f\left(t\right).dt={\int }_x^1{t}^2.f\left(t\right).dt+\frac{x^{16}}{8}+\frac{x^6}{3}+A$$$$FindA?$$

Commented by john santu last updated on 17/May/20

$$\mathrm{f}\left(\mathrm{x}\right)=-{\mathrm{x}}^2\mathrm{f}\left(\mathrm{x}\right)+{2\mathrm{x}}^{15}+{2\mathrm{x}}^5$$$$\mathrm{f}\left(\mathrm{x}\right)=\frac{{2\mathrm{x}}^{15}+{2\mathrm{x}}^5}{1+{\mathrm{x}}^2}=\frac{2{\left({\mathrm{x}}^2\right)}^7\mathrm{x}+2{\left({\mathrm{x}}^2\right)}^2\mathrm{x}}{{\mathrm{x}}^2+1}$$$$=\mathrm{g}\left(\mathrm{x}\right)-\frac{4\mathrm{x}}{{\mathrm{x}}^2+1}$$$$\mathrm{A}=-4$$

Commented by redmiiuser last updated on 19/May/20

$$no.$$$$WrongAnswer??$$

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