The integral - 01exsinh xdx-

The correct option is A e^2 3/4 To find : ∫_0^1e^xsin hx dx Since sinh x = #160;e^x e^ x2 So, #160; ∫_0^1e^xsin hx dx = #160;∫_0^1e^2 ...

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Standard XII

Physics

Limitation of Dimensional Analysis

The integral ...

Question

The integral $\int_{0}^{1} e^{x} sinh x d x =$

\frac{e^{2} - 3}{4}

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\frac{e^{2} + 3}{4}

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4 (e^{2} + 3)

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\frac{e^{2} - 5}{4}

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Solution

The correct option is A $\frac{e^{2} - 3}{4}$
To find : $\int_{0}^{1} e^{x} sin h x d x$
Since $sinh x = \frac{e^{x} - e^{- x}}{2}$
So, $\int_{0}^{1} e^{x} sin h x d x = \int_{0}^{1} \frac{e^{2 x} - 1}{2} d x$
$= (\frac{e^{2}}{4} - \frac{1}{2}) - \frac{1}{4}$
$= \frac{(e^{2} - 3)}{4}$
Hence, option 'A' is correct.

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The integral ∫10exsinhxdx=

The correct option is A e2−34To find : ∫10exsinhxdxSince sinhx=ex−e−x2So, ∫10exsinhxdx=∫10e2x−12dx=(e24−12)−14=(e2−3)4Hence, option 'A' is correct.

The integral $\int_{0}^{1} e^{x} sinh x d x =$