Question

Which of the following values represent the definite integral 

$\intop\begin{matrix} 1 \\ 0 \end{matrix}$ $sqrt(1- x^2) dx$

1) $\pi/2$

2) $\pi/3$

3) $\pi/3$

4) $3\pi/4$

Answer 1

$\int^1_0 \sqrt{1-x^2}dx\\=[\frac{x}{2}\sqrt{1-x^2}+\frac{1}{2}sin^{-1}(x)]^1_0\\ =\frac{\pi}{4}$

reference:

1)

https://www.stumblingrobot.com/2015/10/22/use-integration-by-parts-to-establish-formulas-for-the-integral-of-the-square-root-of-1-x2/

2)

https://www.emathzone.com/tutorials/calculus/integral-of-1-over-square-root-of-1-x2.html