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Evaluating a Double
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Chapter 14 Solutions
EBK MULTIVARIABLE CALCULUS
- Evaluating Polar Integrals In Exercises 9-22, change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. μl pV²-3² 11 12. Jo Jo ra I √a²-x² тугилау dy dx JOJOarrow_forwardUsing polar coordinates, evaluate the integral ſ sin(x² + y²) dA, where R is the region 16 ≤ x² + y² ≤ 64.arrow_forward(b) Evaluate the line integral Jo dzalong the simple closed contour C shown in the diagram. -2 -1 2j o 1 2arrow_forward
- Using polar coordinates, evaluate the integral 1 R sin(x² + y²)dA where R is the region 16 ≤ x² + y² ≤ 49.arrow_forward) Using Green's theorem, convert the line integral f.(6y² dx + 2xdy) to a double integral, where C is the boundary of the square with vertices ±(2, 2) and ±(2,-2). ( do not evaluate the integral)arrow_forwardCalculus Evaluate the following integrals by changing to polar coordinates: Part A) Let R be the region in the first quadrant enclosed by the circle x^2 + y^2 = 16 and the lines x = 0 and y = x. [[ cos(x² + y²)dA Rarrow_forward
- Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 5 ydx + 5x°dy, where Cis the square with vertices (0, 0), (2, 0), (2, 2), and (0, 2) oriented counterclockwise. $5y'dx + 5x'dy = iarrow_forwardUsing polar coordinates, evaluate the integral || J sin sin(x ² + y²)dA where R is the region 16 ≤ x² + y² ≤ 25. Rarrow_forwardulus III |Uni Use Green's Theorem to evaluate the line integral cos (y) dx + x²sin (y) dy along CoS the positively oriented curve C, where C is the rectangle with vertices(0,0), (4, 0), (4, 2) and (0, 2).arrow_forward
- Line integrals Use Green’s Theorem to evaluate the following line integral. Assume all curves are oriented counterclockwise.A sketch is helpful. The circulation line integral of F = ⟨x2 + y2, 4x + y3⟩, where Cis the boundary of {(x, y): 0 ≤ y … sin x, 0 ≤ x ≤ π}arrow_forwardUsing Green's Theorem, calculate the area of the region D bounded by the curve C parametrized by c(t) = (sin 2t, sint), 0arrow_forwardpint Evaluate the double integral I ry dA where D is the triangular region with vertices (0,0), (5, 0), (0, 5).arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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