Area of the region between the graphs of y = 1/(x^2 + 1), y = 1/2

The calculator will try to find the area bounded by $$$y = \frac{1}{x^{2} + 1}$$$, $$$y = \frac{1}{2}$$$, with steps shown.

Curves:

Comma-separated. x-axis is $$$y = 0$$$, y-axis is $$$x = 0$$$.

Lower limit:

Optional.

Upper limit:

Optional.

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Your Input

Find the area of the region bounded by the curves $$$y = \frac{1}{x^{2} + 1}$$$, $$$y = \frac{1}{2}$$$.

Solution

$$$\int\limits_{-1}^{1} \left(\left(\frac{1}{x^{2} + 1}\right) - \left(\frac{1}{2}\right)\right)\, dx = -1 + \frac{\pi}{2}\approx 0.570796326794897$$$

Total area: $$$A = -1 + \frac{\pi}{2}$$$.

Region bounded by y = 1/(x^2 + 1), y = 1/2

Answer

Total area: $$$A = -1 + \frac{\pi}{2}\approx 0.570796326794897$$$A.

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Area of the region between the graphs of $$$y = \frac{1}{x^{2} + 1}$$$, $$$y = \frac{1}{2}$$$

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Solution

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