Converting to Polar Coordinates:
In Exercises 17–26, evaluate the iterated
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Chapter 14 Solutions
Multivariable Calculus
- Converting to a polar integral Integrate ƒ(x, y) = [ln (x2 + y2 ) ]/(x2 + y2) over the region 1<= x2 + y2<= e^2.arrow_forwardConverting to a polar integral Integrate ƒ(x, y) = [ln (x2 + y2 ) ]/sqrt(x2 + y2) over the region 1<= x2 + y2<= e.arrow_forwardFind ʃR (x2 + y2) dA where R is the region 4 ≤ (x2 + y2)≤ 9. Hint: Use polar coordinates.arrow_forward
- How do you solve this triple integral? triple integral(Fdxdydz) where F = z/((x^2 + y^2 + z^2)^3/2). x = (-1,1), y = (-1,1), z = (0,1). Do you have to use polar coordinates or can you do it in cartesian?arrow_forwardTranslation of text in image: where R is the region of the XY plane, given by R = R1 ∪ R2, and represented in the attached graph When transforming the previous integral applying the change of variable to polar coordinates, we obtain:arrow_forwardA. State the F undamental Theorem of Calculus for Line Integrals. B. Let f(x, y, z) = xy + 2yz + 3zx and F = grad f. Find the line integral of F along the line C with parametric equations x = t, y = t, z = 3t, 0 ≤ t ≤ 1. You must compute the line integral directly by using the given parametrization. C. Check your answer in Part B by using the Fundamental Theorem of Calculus for Line Integrals.arrow_forward
- A. State the Fundamental Theorem of Calculus for Line Integrals. B. Let f(x, y, z) = x^2 + 2y^2 + 3z^2 and F = grad f. Find the line integral of F along the line C with parametric equations x = 1 + t, y = 1 + 2t, z = 1 + 3t, 0 ≤ t ≤ 1. You must compute the line integral directly by using the given parametrization. C. Check your answer in Part B by using the Fundamental Theorem of Calculus for Line Integrals.arrow_forwardShow all solution. Include the graph and figures. Evaluate the iterated double integral using polar coordinates.arrow_forwardDouble integral to line integral Use the flux form of Green’sTheorem to evaluate ∫∫R (2xy + 4y3) dA, where R is the trianglewith vertices (0, 0), (1, 0), and (0, 1).arrow_forward
- Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. Cartesian in images* I need the answer for the boxes 1, 2, and 3 and the value of the doublearrow_forwarda) Sketch the region of integration b) Express the region in polar coordinates c) Write an equivalent double integral in polar coordinatesarrow_forwardDouble integrals in polar coordinates: Evaluate the iterated integral by converting to polar coordinates. ⌠2⌠√(2x-x²) 4√(x2+y2) dy dx ⌡0⌡0arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning