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Evaluating an Improper Iterated
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Calculus: Early Transcendental Functions
- Evaluating Triple Iterated Integrals Evaluate the integrals in Exercises 7-20 1 cl cl 12. 0 J K x²+3x₂² Jo 2 3-3x-y o Jo 2 LI S ~ 0 2 → dx (x+y+z) dy dx dzarrow_forward²6² F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. Je (4z + 4y) dx + (4x − 2z) dy + (4x − 2y) dz (a) C: line segment from (0, 0, 0) to (1, 1, 1) Evaluate (b) C: line segment from (0, 0, 0) to (0, 0, 1) to (1, 1, 1) (c) C: line segment from (0, 0, 0) to (1, 0, 0) to (1, 1, 0) to (1, 1, 1)arrow_forwardUse 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_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_forwardUse 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_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
- Using the method of u-substitution, | (32 – 8)² dz = | f(u) du - where u = (enter a function of æ) du = da (enter a function of ¤) a = (enter a number) b = (enter a number) f(u) = (enter a function of u). The value of the original integral isarrow_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_forwardсп show that f(x=3x is integralble [0,4] using the definition.arrow_forward
- The 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_forwarde* What is the integrable form of dx? A du B du du D duarrow_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_forward
- Calculus 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