$$\int_{2}^{7}(2 $\pi$ $(\sqrt{1+e^x/5})$ ) dx$$

asked by guest
on Nov 13, 2024 at 8:55 pm



You asked:

Evaluate the integral: \(\int_{2}^{7}{2 \cdot \pi \cdot \sqrt{1 + \frac{{e}^{x}}{5}}}dx\)

MathBot Answer:

Definite integral

\[\int_{2}^{7}{2 \cdot \pi \cdot \sqrt{1 + \frac{{e}^{x}}{5}}}dx = - 2 \pi \left(- \log{\left(1 + \sqrt{1 + \frac{e^{2}}{5}} \right)} + 2 \sqrt{1 + \frac{e^{2}}{5}} + \log{\left(-1 + \sqrt{1 + \frac{e^{2}}{5}} \right)}\right) + 2 \pi \left(- \log{\left(1 + \sqrt{1 + \frac{e^{7}}{5}} \right)} + 2 \sqrt{1 + \frac{e^{7}}{5}} + \log{\left(-1 + \sqrt{1 + \frac{e^{7}}{5}} \right)}\right) \approx 175.32658584740695148624218115134087\]

\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).

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