What is the integral from 1 to 100 of 1/(1+x^2) ?

The integral from 1 to 100 of 1/(1+x^2) is arctan(100)-pi/4

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integral from 1 to 100 of 1/(1+x^2)

\int_{1}^{100} \frac{1}{1 + x ^{2}} d x

arctan (100) - \frac{π}{4}

Decimal

0.77539 \dots

Solution steps

\int_{1}^{100} \frac{1}{1 + x ^{2}} d x

Use the common integral:

\int \frac{1}{1 + x ^{2}} d x = arctan (x)

= [arctan (x)]_{1}^{100}

Compute the boundaries:

arctan (100) - \frac{π}{4}

= arctan (100) - \frac{π}{4}

What is the integral from 1 to 100 of 1/(1+x^2) ?
The integral from 1 to 100 of 1/(1+x^2) is arctan(100)-pi/4