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

The integral from 0 to 1 of (1-cos(x))/(x^2) is 0.48638…

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integral from 0 to 1 of (1-cos(x))/(x^2)

\int_{0}^{1} \frac{1 - cos ( x )}{x ^{2}} d x

0.48638 \dots

Solution steps

\int_{0}^{1} \frac{1 - cos ( x )}{x ^{2}} d x

Apply Integration By Parts

= [- \frac{1 - cos ( x )}{x} - \int - \frac{sin ( x )}{x} d x]_{0}^{1}

\int - \frac{sin ( x )}{x} d x = - Si (x)

= [- \frac{1 - cos ( x )}{x} - (- Si (x))]_{0}^{1}

Simplify

= [- \frac{1 - cos ( x )}{x} + Si (x)]_{0}^{1}

Compute the boundaries:

0.48638 \dots

= 0.48638 \dots

What is the integral from 0 to 1 of (1-cos(x))/(x^2) ?
The integral from 0 to 1 of (1-cos(x))/(x^2) is 0.48638…