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

The integral from-1 to 1 of 1/(sqrt(1+x^2)) is ln(sqrt(2)+1)-ln(sqrt(2)-1)

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

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

ln (2 + 1) - ln (2 - 1)

Decimal

1.76274 \dots

Solution steps

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

Use the common integral:

\int \frac{1}{1 + x ^{2}} d x = ln x^{2} + 1 + x

= [ln x^{2} + 1 + x]_{- 1}^{1}

Compute the boundaries:

ln (2 + 1) - ln (2 - 1)

= ln (2 + 1) - ln (2 - 1)

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What is the integral from-1 to 1 of 1/(sqrt(1+x^2)) ?
The integral from-1 to 1 of 1/(sqrt(1+x^2)) is ln(sqrt(2)+1)-ln(sqrt(2)-1)