যোজিতফল নির্ণয় কর: $\int_{0}^{1 n 2} \frac{e^{x} d x}{1 + e^{x}}$

Created: 2 years ago | Updated: 2 years ago

Updated: 2 years ago

1 n \frac{3}{2}

ব্যাখ্যা

214

Best Ans:

$\int_{0}^{\ln 2} \frac{e^{x} d x}{1 + e^{x}}$

$= \int_{0}^{\ln 2} \frac{d (1 + e^{x})}{1 + e^{x}} [∵ d (1 + e^{x}) = 0 + e^{x} d x = e^{x} d x]$

$= {[\ln (1 + e^{x})]}_{0}^{\ln 2}$

$= l n (1 + e^{\ln 2}) - l n (1 + e^{0})$

$= l n (1 + 2) - l n (1 + 1)$

$= l n 3 - l n 2$

$= l n \frac{3}{2} (A n s .)$

1 year ago

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Almumen

সমতলে বস্তুকণার গতি (Motion of particles in a plane)

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