What is the area under the curve in the interval [2,7] for the function $\frac{1}{{(1 + x^{2})}^{\frac{1}{2}}}$ $1/(1 + x^2)^(1/2)$ ?

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What is the area under the curve in the interval [2,7] for the function $\frac{1}{{(1 + x^{2})}^{\frac{1}{2}}}$ $1/(1 + x^2)^(1/2)$ ?

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Answer 1 · 2015-08-19T15:58:53

$\int_{2}^{7} \frac{1}{\sqrt{1 + x^{2}}} d x = {sinh}^{- 1} (7) - {sinh}^{- 1} (2) = 1.20$ $int_2^7 1/sqrt(1+x^2) dx = sinh^-1 (7)- sinh^-1 (2) = 1.20$ (3sf)

Explanation:

$\int_{2}^{7} \frac{1}{\sqrt{1 + x^{2}}} d x = {sinh}^{- 1} x ∣_{2}^{7} = {sinh}^{- 1} (7) - {sinh}^{- 1} (2)$ $int_2^7 1/sqrt(1+x^2) dx = sinh^(-1) x|_2^7 = sinh^-1 (7)- sinh^-1 (2)$

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What is the area under the curve in the interval [2,7] for the function $\frac{1}{{(1 + x^{2})}^{\frac{1}{2}}}$ $1/(1 + x^2)^(1/2)$ ?

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