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Question-189382




Question Number 189382 by TUN last updated on 15/Mar/23
Answered by Ar Brandon last updated on 15/Mar/23
Use integration by parts with;  a. u(x)=x^3 +1 and v′(x)=e^(3x−2)   b. u(x)=3x^2 −x+2 and v′(x)=e^(x−2)   c. u(x)=x^4 −2x and v′(x)=sin(3−x)  d. u(x)=cos(πx) and v′(x)=e^(2x)
$$\mathrm{Use}\:\mathrm{integration}\:\mathrm{by}\:\mathrm{parts}\:\mathrm{with}; \\ $$$${a}.\:\mathrm{u}\left({x}\right)={x}^{\mathrm{3}} +\mathrm{1}\:\mathrm{and}\:\mathrm{v}'\left({x}\right)={e}^{\mathrm{3}{x}−\mathrm{2}} \\ $$$${b}.\:\mathrm{u}\left({x}\right)=\mathrm{3}{x}^{\mathrm{2}} −{x}+\mathrm{2}\:\mathrm{and}\:\mathrm{v}'\left({x}\right)={e}^{{x}−\mathrm{2}} \\ $$$${c}.\:\mathrm{u}\left({x}\right)={x}^{\mathrm{4}} −\mathrm{2}{x}\:\mathrm{and}\:\mathrm{v}'\left({x}\right)=\mathrm{sin}\left(\mathrm{3}−{x}\right) \\ $$$${d}.\:\mathrm{u}\left({x}\right)=\mathrm{cos}\left(\pi{x}\right)\:\mathrm{and}\:\mathrm{v}'\left({x}\right)={e}^{\mathrm{2}{x}} \\ $$

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