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Question Number 181792 by zainaltanjung last updated on 30/Nov/22

Please Calculate this integration 2∫_0 ^1 dx ∫_(2x) ^((2x)^(1/3) ) dy

$$\mathrm{Please}\:\mathrm{Calculate}\:\mathrm{this}\:\mathrm{integration} \\ $$$$\mathrm{2}\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{dx}\:\underset{\mathrm{2x}} {\overset{\left(\mathrm{2x}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} } {\int}}\:\mathrm{dy} \\ $$

Commented by Frix last updated on 30/Nov/22

2∫_0 ^1 dx∫_(2x) ^((2x)^(1/3) ) dy means 2(∫_0 ^1 dx)×(∫_(2x) ^((2x)^(1/3) ) dy) Or do you mean this: 2∫_0 ^1 ∫_(2x) ^((2x)^(1/3) ) dydx=2∫_0 ^1 (∫_(2x) ^((2x)^(1/3) ) dy)dx

$$\mathrm{2}\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{dx}\underset{\mathrm{2}{x}} {\overset{\left(\mathrm{2}{x}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} } {\int}}{dy}\:\mathrm{means}\:\mathrm{2}\left(\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{dx}\right)×\left(\underset{\mathrm{2}{x}} {\overset{\left(\mathrm{2}{x}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} } {\int}}{dy}\right) \\ $$$$\mathrm{Or}\:\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{this}: \\ $$$$\mathrm{2}\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\underset{\mathrm{2}{x}} {\overset{\left(\mathrm{2}{x}\overset{\frac{\mathrm{1}}{\mathrm{3}}} {\right)}} {\int}}{dydx}=\mathrm{2}\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\left(\underset{\mathrm{2}{x}} {\overset{\left(\mathrm{2}{x}\overset{\frac{\mathrm{1}}{\mathrm{3}}} {\right)}} {\int}}{dy}\right){dx} \\ $$

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