Mathematics

You're finding the area of a circular segment—the region "cut off" by a vertical line. The key is to set up an integral that captures the curved boundary of the circle above the $x$-axis, from where the line $x=1$ intersects it to the rightmost point. Recognizing that $x^2+y^2=4$ gives you $y=\sqrt{4-x^2}$ in the upper half, you can integrate this function over the appropriate $x$-interval, or use a geometric approach combining a circular sector and a triangle.

You're finding the area of a circular segment—the region "cut off" by a vertical line. The key is to set up an integral that captures the curved boundary of the circle above the $x$-axis, from where the line $x=1$ intersects it to the rightmost point. Recognizing that $x^2+y^2=4$ gives you $y=\sqrt{4-x^2}$ in the upper half, you can integrate this function over the appropriate $x$-interval, or use a geometric approach combining a circular sector and a triangle.