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Question Number 100207 by Rio Michael last updated on 25/Jun/20

$$\mathrm{Given}\mathrm{an}\mathrm{even}\mathrm{fuction}f\left(x\right)\mathrm{such}\mathrm{that}{\stackrel{a}{\int }}_{-a}f\left(x\right)dx=\sqrt{a}\mathrm{\forall }a⩾0$$$$\mathrm{find}{\int }_3^{4}f\left(x\right)dx$$$$$$

Commented by mr W last updated on 25/Jun/20

$${\int }_0^{a}f\left(x\right)dx=\frac{\sqrt{a}}{2}$$$${\int }_0^{4}f\left(x\right)dx=\frac{\sqrt{4}}{2}=1$$$${\int }_0^{3}f\left(x\right)dx=\frac{\sqrt{3}}{2}$$$${\int }_3^{4}f\left(x\right)dx={\int }_0^4-{\int }_0^3=1-\frac{\sqrt{3}}{2}$$

Commented by Rio Michael last updated on 25/Jun/20

$$\mathrm{perfect}\mathrm{sir}$$

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