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Question Number 199934 by cortano12 last updated on 11/Nov/23

$$\cancel{\underset{―}{\underbrace{}}}$$$$$$

Answered by mr W last updated on 11/Nov/23

$${\int }_0^{3}f\left(x\right)dx=a,say$$$${\int }_0^3\frac{f\left(3x\right)}{3}dx=a$$$$\frac{1}{9}{\int }_0^{3}f\left(3x\right)d\left(3x\right)=a$$$$\frac{1}{9}{\int }_0^{9}f\left(t\right)dt=a$$$$\frac{1}{9}{\int }_0^9\frac{f\left(3t\right)}{3}dt=a$$$$\frac{1}{9\times 9}{\int }_0^{9}f\left(3t\right)d\left(3t\right)=a$$$$\frac{1}{9\times 9}{\int }_0^{27}f\left(u\right)du=a$$$$\frac{1}{9\times 9}[{\int }_0^{3}f\left(x\right)dx+{\int }_3^{27}f\left(x\right)dx]=a$$$$\frac{1}{9\times 9}[a+10]=a$$$$10=80a$$$$\Rightarrow a=\frac{1}{8}$$

Answered by cortano12 last updated on 11/Nov/23

$$\underbrace{⋐}$$

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