Find the range of the function integral calculus bc

Question

Find the range of the function  . (5 points)

answer choices

	[0, 4π]
	[0, π]
	[-4, 0]
	[0, 4]

Answer 1

√(4 - t²) from 0 to and up is a quarter circle with radius 2. The integral is the area under the curve or the area of a quarter circle with radius 2. The area of that quarter circle is πr²/4 = π(2²)/4 = π so no matter what "x" is, the largest the area can be is π and, of course, the smallest it can be is zero.