What is the integral from 0 to 1 of arcsin(y) ?

The integral from 0 to 1 of arcsin(y) is pi/2-1

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integral from 0 to 1 of arcsin(y)

\int_{0}^{1} arcsin (y) d y

\frac{π}{2} - 1

Decimal

0.57079 \dots

Solution steps

\int_{0}^{1} arcsin (y) d y

Apply Integration By Parts

: [y arcsin (y) - \int \frac{y}{1 - y ^{2}} d y]_{0}^{1}

= [y arcsin (y) - \int \frac{y}{1 - y ^{2}} d y]_{0}^{1}

\int \frac{y}{1 - y ^{2}} d y = - 1 - y^{2}

= [y arcsin (y) - (- 1 - y^{2})]_{0}^{1}

Simplify

= [y arcsin (y) + 1 - y^{2}]_{0}^{1}

Compute the boundaries:

\frac{π}{2} - 1

= \frac{π}{2} - 1

\int_{\frac{π}{2}}^{π} (1 + cos (x))^{2} d x

\int_{0}^{2} - 5 - x^{2} d x

\int_{0}^{1} 630 x^{4} (1 - x)^{4} d x

\int_{- 6}^{6} x^{3} d x

\int_{0}^{2 π} \frac{sin ( x )}{x} d x

What is the integral from 0 to 1 of arcsin(y) ?
The integral from 0 to 1 of arcsin(y) is pi/2-1