Dick said:Yes, if you fix the unmatched parenthesis which makes it look a little confusing. The outer radius of the washer is 2 and the inner radius is (2-sqrt(x)).
elitespart said:oh whoops forgot to add a bracket at the end. Thanks for your help.
Dick said:No, y^2=x gives y=sqrt(x) or y=-sqrt(x). Those are the boundaries of the region. Your original answer would be ok if they had specified y=0 as a boundary. But they didn't.
elitespart said:oh okay. So would y=2 factor into the outer radius too? Meaning r = [2 - (-sqrt(x))]?
The Washer Method problem is a mathematical concept used in calculus to find the volume of an irregularly shaped solid formed by rotating a curve around an axis.
The Washer Method involves finding the volume of a solid by taking the integral of the area of a cross section of the solid, which is then multiplied by the thickness of the solid and integrated over the given interval.
The Washer Method and the Shell Method both involve finding the volume of a solid of revolution, but they use different techniques. The Washer Method involves slicing the solid into cross sections perpendicular to the axis of rotation, while the Shell Method involves slicing the solid into cylindrical shells parallel to the axis of rotation.
Common mistakes when using the Washer Method include using the wrong formula, not properly setting up the integral, and not correctly identifying the limits of integration.
To improve your understanding and skills in solving Washer Method problems, it is important to practice using the method with various types of curves, pay attention to the setup of the integral, and seek help from a tutor or teacher if needed.