What is the integral from 0 to 1 of (1+x^2)/(1+y^2) ?

The integral from 0 to 1 of (1+x^2)/(1+y^2) is (1+x^2) pi/4

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integral from 0 to 1 of (1+x^2)/(1+y^2)

\int_{0}^{1} \frac{1 + x ^{2}}{1 + y ^{2}} d y

(1 + x^{2}) \frac{π}{4}

Solution steps

\int_{0}^{1} \frac{1 + x ^{2}}{1 + y ^{2}} d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= (1 + x^{2}) \cdot \int_{0}^{1} \frac{1}{1 + y ^{2}} d y

\int_{0}^{1} \frac{1}{1 + y ^{2}} d y = \frac{π}{4}

= (1 + x^{2}) \frac{π}{4}

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What is the integral from 0 to 1 of (1+x^2)/(1+y^2) ?
The integral from 0 to 1 of (1+x^2)/(1+y^2) is (1+x^2) pi/4