Evaluating an Improper Iterated
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Chapter 14 Solutions
Calculus (MindTap Course List)
- Use Green's Theorem to evaluate · F · dr, where F(x, y) = = with vertices (-3,-9), (5,-9), (5,2), and (-3,2). The integral obtained from from Green's Theorem is J dA where D is the interior of the rectangle. This evaluates to (3xy, y 8 +9) and C is the rectanglearrow_forwardevaluating V-2 by substitution, if u =x– 2 then what will be the resulting indefinite In integral in terms of u and du? 3/2_ np 2u np 3/2. +u duarrow_forwardEvaluating 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_forward
- Evaluate 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_forwardThe figure shows the sales growth rates under different levels of distribution and advertising from a to b. Set up an integral to determine the extra sales growth if $3 million is used in advertising rather than $2 million. (Use f for f(x), g for g(x), and h for h(x).) $4 Million advertising $3 Million 8 advertising $2 Million h advertising a Distribution dx Need Help? Read It Sales Growth Ratearrow_forwardUsing the method of u-substitution, 5 [²(2x - 7)² de where U = du: = a = b = f(u) = = ·b [ f(u) du a It (enter a function of x) da (enter a function of ä) (enter a number) (enter a number) (enter a function of u). The value of the original integral is 9.arrow_forward
- сп show that f(x=3x is integralble [0,4] using the definition.arrow_forwardUsing the Fundamental Theorem of Line Integrals In Exercises 47-50, evaluate F· dr using the Fundamental Theorem of Line Integrals. F (x, y) = e²*i + e²»j C : line segment from (-1, –1) to (0,0)arrow_forwardEvaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 5y'dx + 4x°dy, where Cis the square with vertices (0, 0), (1, 0). (1, 1), and (0, 1) oriented counterclockwise. f 5y'dx + 4x°dy iarrow_forward
- e* What is the integrable form of dx? A du B du du D duarrow_forwardEvaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 5 y²dx + 6 x²dy, where C is the square with vertices (0, 0), (2, 0), (2, 2), and (0, 2) oriented counterclockwise. f 5 y²dx + 6x²dy =arrow_forwardEvaluating a Double Integral by Converting from Rectangular Coordinates [[ (x + y) dA where R (x + y) dA where R = {(x, y)|1 ≤ x² + y² ≤ 4, x ≤ 0} . R Evaluate the integralarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning