Welcome to mathhomeworkanswers.org. Start by asking a new question, answering unanswered questions or registering or a free account!
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!

Most popular tags

algebra problems solving equations word problems calculating percentages geometry problems calculus problems math problem fraction problems trigonometry problems rounding numbers simplifying expressions solve for x order of operations pre algebra problems please help me to answer this step by step. algebra please answer this queastion as soon as possible. thank you :) evaluate the expression slope intercept form probability plz. give this answer as soon as possible factoring word problem statistics problems polynomials solving inequalities how to find y intercept logarithmic equations help algebra 2 problems equation of a line sequences and series solving systems of equations by substitution 6th grade math dividing fractions greatest common factor square roots graphing linear equations geometric shapes long division help me!! solving systems of equations substitution method least common multiple factoring polynomials least to greatest proving trigonometric identities dividing decimals ratio and proportion solving equations with fractions trig identity standard form of an equation http: mathhomeworkanswers.org ask# function of x algebra problem help me precalculus problems ( solving equations with variables on both sides algebraic expressions slope of a line through 2 points i need help with this domain of a function solving systems of equations by elimination college algebra distributive property solving quadratic equations trinomial factoring factors of a number perimeter of a rectangle slope of a line greater than or less than division fraction word problems exponents differentiation differential equation how to find x intercept 8th grade math limit of a function fractions algebra word problems equivalent fractions math algebra 1 hw help asap simplifying fractions elimination method geometry 7th grade math inverse function . area of a triangle geometry 10th grade please answer this question as soon as possible. thank you :) story problems simplify integral area of a circle systems of equations containing three variables standard deviation what is the answers? circumference of a circle place value solving triangles width of a rectangle parallel lines solving linear equations mixed numbers to improper fractions percentages scientific notation problems zeros of a function homework prime factorization number of sides of a polygon area of a rectangle calculus length of a rectangle 5th grade math solving systems of equations by graphing quadratic functions lowest common denominator percents mathematical proofs ratios diameter of a circle dividing polynomials vertex of a parabola derivative of a function equation algebra 1 integers evaluating functions converting fractions to decimals ) combining like terms algebra 2 range of a function perpendicular lines finding the nth term least common denominator ordered pairs calculators find out the answer calculus problem radius of a circle greatest to least unit conversion solve for y math homework complex numbers slope because i don't understand functions geometry word problems area word problems 4th grade math solving radical equations multiplying fractions statistics equation of a tangent line calculate distance between two points help me please and show how to work it out = common denominator binomial expansion absolute value round to the nearest tenth #math simplifying radicals () set builder notation help!!!. show every step to solve this problem significant figures show work adding fractions product of two consecutive numbers radicals (explain this to me) solve what is the answer? - number patterns midpoint of a line median graphing roots of polynomials place values divisibility rules pre-algebra problems graphing functions volume of a cylinder subtracting fractions 1 ? factor by grouping maths decimals improper fractions to mixed numbers percentage how to complete the square simultaneous equations derivatives expanded forms rational irrational numbers simplifying trigonometric equation using identities sets numbers compound interest solving equations with variables divide need help solving quadratic equations by completing the square comparing decimals implicit differentiation logarithms integration rounding decimals surface area of a prism multiplying polynomials trigonometry #help http: mathhomeworkanswers.org ask?cat=# please help algebra1 angles how do you solve this problem in distributive property http: mathhomeworkanswers.org ask# age problem probability of an event perimeter of a triangle solving trigonometric equations mixed numbers pemdas arithmetic sequences surface area of a cube average rate of change chemistry matrices fraction geometry problem rounding to the nearest cent height of a triangle 9th grade math dividing factor 5th grade math problems direct variation mean

Find the volume of the solid generated by revolving the region bounded about the x-axis.

Use the washer method.


asked Jul 1, 2012 in Calculus Answers by anonymous

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:

To avoid this verification in future, please log in or register.

1 Answer

The two curves (one a U shape, the other an inverted U) intersect at the solution to the equation x^2+2=-x^2+2x+6. This reduces to the quadratic 2x^2-2x-4=0 which becomes x^2-x-2=0. This factorises (x+1)(x-2)=0 so the solutions are -1 and 2, and y=3 and 6. The bounds are limited by the requirement 0<=x<=3. Therefore the bounds for the volume captured by the two curves are 0<=x<=2.
Consider first the volume of rotation of the inverted U, the superior curve, y=-2x^2+2x+6 for 0<=x<=2. Consider the disc width dx standing on its side with radius y. The volume of the disc is (pi)y^2dx=(pi)(-x^2+2x+6)^2dx. A stack of such discs placed on its side is the volume between the curve and the x axis. So we need to integrate (pi)(x^4-4x^3-8x^2+24x+36)dx for 0<=x<=2. That is, (pi)[x^5/5-x^4-8x^3/3+12x^2+36x] for 0<=x<=2.
Now we have to do the same for the other curve y=x^2+2. The volume of the thin disc is (pi)(x^2+2)^2dx=(pi)(x^4+4x^2+4)dx. This integrates as (pi)[x^5/5+4x^3/3+4x] for 0<=x<=2.
Combine the two volumes by subtracting the latter from the former (inferior from the superior) we get (pi)[-x^4-4x^3+12x^2+32x] for 0<=x<=2. So this evaluates to (pi)(-16-32+48+64)=64(pi)=201.06 cubic units.

answered Oct 19, 2014 by Rod Top Rated User (372,220 points)

Related questions

1 answer 61 views
0 answers 145 views