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Use the result in Exercise 31 to show that the
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- 5. Prove that the equation has no solution in an ordered integral domain.arrow_forwardIf x and y are elements of an ordered integral domain D, prove the following inequalities. a. x22xy+y20 b. x2+y2xy c. x2+y2xyarrow_forwardFind a piecewise smooth parametrization of the path C (the edges of the triangle in space with vertices: (0,0,0), (0, 1,0), and (0,1,1)). Then evaluate the line integral √(2x² + y² − 2) ds. -arrow_forward
- please answerarrow_forward3. Evaluate the line integral (3ry² + 6y) dr, where C is the path traced by first moving from the с point (-3, 1) to the point (2, 1) along a straight line, then moving from the point (2, 1) to the point (5,2) along the parabola x = = y² + 1.arrow_forwardhelp me asap pls for number 1arrow_forward
- Calculate the line integral f(3xy³ − 4x + 4y + 8) dx + (−3xy+5) dy, where C' is the rectangle with vertices (2, −4), (2, -3), (−3,−3), and (−3,-4) oriented clockwise. Enter an exact answer. Provide your answer below: f(3x³ 4x + 4y + 8) dx + (−3xy + 5) dy =arrow_forwardUse the given transformation to evaluate the integral. x - /| 2 Y dA, where R is the parallelogram enclosed by the lines x - 4y = 0, x - 4y = 2, 6x - y = 4, and 6x - y = 5; u = x - 4y, v = 6x – y 6x – yarrow_forwardLet C be the closed, piecewise smooth curve formed by traveling in straight lines between the points (−4, 2), (−4, −3), (2, −2), (2, 7), and back to (-4, 2), in that order. Use Green's theorem to evaluate the following integral. Jo (2xy) dx + (xy2) dyarrow_forward
- Calculate the line integral f (2x²y + 10x + 6y − 6) dx + (−6xy + 7) dy, - where C' is the rectangle with vertices (−1, 1), (−1, 2), (-4,2), and (-4, 1) oriented clockwise. Enter an exact answer. Provide your answer below: fc(2x²y + 10x + 6y - 6) dx + (−6xy + 7) dy =arrow_forwardLet C be the closed, piecewise smooth curve formed by traveling in straight lines between the points (−4, 2), (−4, −3), (2, −2), (2, 7), and back to (−4, 2), in that order. Use Green's theorem to evaluate the following integral. √ (2xY) (2xy) dx + (xy2) dyarrow_forwardUse a substitution of u = r2 to integrate dr. 1+r4arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningElements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,