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Proposition: Integral of Inverse Sine

Let $-1 < a < b < 1$. The Riemann-integral of the inverse sine $\arcsin(x)$ on the closed real interval is given by the formula

$$\int_a^b\arcsin(x)dx= \left(x\arcsin(x)+\sqrt{1-x^2}\right)\;\begin{array}{|l}a\\\\b\end{array}.$$

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References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983