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Question Number 92608 by jagoll last updated on 08/May/20

Commented by john santu last updated on 08/May/20

$$\mathrm{g}\left(\mathrm{t}\right)=\{\begin{array}{l}-\frac{1}{2}\mathrm{t},-4⩽\mathrm{t}⩽0\\ -\sqrt{9-{(\mathrm{t}-3)}^2},0⩽\mathrm{t}⩽6\\ 3,6<\mathrm{t}⩽8\end{array}$$$$\mathrm{f}\left(\mathrm{x}\right)=3\mathrm{x}+\underset{0}{\stackrel{\mathrm{x}}{\int }}\mathrm{g}\left(\mathrm{t}\right)\mathrm{dt}$$$$\mathrm{f}\left(\mathrm{x}\right)=3\mathrm{x}+\{\begin{array}{l}-\frac{1}{4}{\mathrm{x}}^2\\ -\frac{9}{2}{\sin }^{-1}\left(\frac{\mathrm{x}-3}{3}\right)-\frac{1}{2}\left(\frac{\mathrm{x}-3}{3}\right)\sqrt{6\mathrm{x}-{\mathrm{x}}^2}+\frac{9\pi }{4}\\ 6\mathrm{x}\end{array}$$

Commented by jagoll last updated on 08/May/20

$$\mathrm{find}\mathrm{f}\left(\mathrm{x}\right)=3\mathrm{x}+\underset{0}{\stackrel{\mathrm{x}}{\int }}\mathrm{g}\left(\mathrm{t}\right)\mathrm{dt}$$$$\mathrm{graph}\mathrm{g}\left(\mathrm{x}\right)\mathrm{it}\mathrm{shown}\mathrm{above}$$

Commented by MJS last updated on 08/May/20

$$\underset{t}{\int }...dt\mathrm{is}\mathrm{not}\mathrm{possible}$$

Commented by jagoll last updated on 08/May/20

$$\mathrm{why}\mathrm{sir}?$$$$\mathrm{f}\left(\mathrm{x}\right)=3\mathrm{x}+{\int }_0^{\mathrm{x}}\mathrm{g}\left(\mathrm{t}\right)\mathrm{dt}\mathrm{sir}$$

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