What is the integral from 0 to 1 of (arctan(x)) ?

The integral from 0 to 1 of (arctan(x)) is pi/4-1/2 ln(2)

Popular >

integral from 0 to 1 of (arctan(x))

\int_{0}^{1} (arctan (x)) d x

\frac{π}{4} - \frac{1}{2} ln (2)

Decimal

0.43882 \dots

Solution steps

\int_{0}^{1} arctan (x) d x

Apply Integration By Parts

: [x arctan (x) - \int \frac{x}{x ^{2} + 1} d x]_{0}^{1}

= [x arctan (x) - \int \frac{x}{x ^{2} + 1} d x]_{0}^{1}

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

= [x arctan (x) - \frac{1}{2} ln x^{2} + 1]_{0}^{1}

Compute the boundaries:

\frac{π}{4} - \frac{1}{2} ln (2)

= \frac{π}{4} - \frac{1}{2} ln (2)

\int_{0}^{3} π x d x

\int_{0}^{\frac{π}{3}} (10 sec^{2} (x)) d x

\int_{0}^{π} sin (t) cos^{2} (t) d t

\int_{0}^{x^{3}} e^{- t} d t

\int_{3}^{6} (2 x + 1) e^{0.4 x} d x

What is the integral from 0 to 1 of (arctan(x)) ?
The integral from 0 to 1 of (arctan(x)) is pi/4-1/2 ln(2)