Antiderivative of a square root

Substitute , so that . The integral is then equivalent to

In general, , so .

We want the substitution made above to be reversible, so that . This restricts to the interval , and over this interval we have , so we take the positive square root in order that .

Then the integral becomes

which can be computed in several ways. One method is to integrate by parts, taking

so that

Then with , you have and , which follows from the Pythagorean identity. So

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere

345

step-by-step explanation: