Evaluating a Double
In Exercises 9–-16, evaluate the double integral
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Chapter 14 Solutions
Calculus: Early Transcendental Functions
- Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 2y dx + 3x²dy, where Cis the square with vertices (0, 0), (2, 0), (2, 2), and (0, 2) oriented counterclockwise. O 2y dx + 3x²dy = iarrow_forwardEvaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 5 y dx + 5 x?dy, where Cis the square with vertices (0, 0), (3, 0), (3, 3), and (0, 3) oriented counterclockwise. $ 5 y'dx + 5x°dy iarrow_forwardry dA where D is the triangular region with vertices (0,0), (1,0), (0,3) Evaluate the double integral I = Darrow_forward
- Use Green's Theorem to evaluate the following integral Let² dx + (5x + 9) dy Where C is the triangle with vertices (0,0), (11,0), and (10, 9) (in the positive direction).arrow_forwardUsing Green's Theorem, find the outward flux of F across the closed curve C.F = (-5x + 2y) i + (6x - 9y) j; C is the region bounded above by y = -5x 2 + 250 and below by y=5x2 in the first quadrantarrow_forwardEvaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $43 4 y²dx + 5 x²dy, where Cis the square with vertices (0, 0), (3, 0), (3, 3), and (0, 3) oriented counterclockwise. f4y³dx + 5x²dy = + iarrow_forward
- Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. P y*dx + 2x²dy, where C is the square with vertices (0, 0), (3, 0), (3, 3), and (0, 3) oriented counterclockwise. P y'dx + 2x*dy :arrow_forwardHow do you find the area of a region 0 ≤ r1(θ) ≤ r ≤ r2(θ),a≤ θ ≤ b, in the polar coordinate plane? Give examples.arrow_forwardEvaluate the line integral using Green's Theorem and check the answer by evaluating it directly. ∮C6 y2dx+3 x2dy∮C6 y2dx+3 x2dy, where CC is the square with vertices (0,0)(0,0), (3,0)(3,0), (3,3)(3,3), and (0,3)(0,3) oriented counterclockwise.arrow_forward
- Use Green's Theorem to evaluate the line integral. | 3x2eY dx + eY dy C C: boundary of the region lying between the squares with vertices (1, 1), (-1, 1), (-1, -1), (1, -1) and (8, 8), (-8, 8), (-8, -8), (8, -8)arrow_forwardUse Green's Theorem to evaluate the line integral. C y dx + 7x dy C: square with vertices (0, 0), (0, 1), (1, 0), and (1, 1)arrow_forwardEvaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 6 y²dx + 2x²dy, where Cis the square with vertices (0, 0), (2, 0), (2, 2), and (0, 2) oriented counterclockwise. foy'dr + 2x*dy = i -128arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,