What is area y= 1/2 x^2, 1/(x^2+1) ?

The answer to area y= 1/2 x^2, 1/(x^2+1) is -1/3+pi/2

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area y= 1/2 x^2, 1/(x^2+1)

area

y = \frac{1}{2} x^{2}, \frac{1}{x ^{2} + 1}

- \frac{1}{3} + \frac{π}{2}

Decimal

1.23746 \dots

Solution steps

Apply the area formula:

\int_{- 1}^{1} \frac{1}{2} x^{2} - \frac{1}{x ^{2} + 1} d x

Solve

\int_{- 1}^{1} \frac{1}{2} x^{2} - \frac{1}{x ^{2} + 1} d x : - \frac{1}{3} + \frac{π}{2}

The area is:

= - \frac{1}{3} + \frac{π}{2}

What is area y= 1/2 x^2, 1/(x^2+1) ?
The answer to area y= 1/2 x^2, 1/(x^2+1) is -1/3+pi/2