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Using the Fundamental Theorem for line
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Calculus: Early Transcendentals (3rd Edition)
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- please show full solution thankyouarrow_forwardQuestion 3 of 15 Use Green's Theorem to evaluate the line integral . F · dr, where F(x, y) = (x²,x²) and C consists of the arcs y = x² and y = 9x for 0 < x < 9. Orient the curve counterclockwise. (Use symbolic notation and fractions where needed.) F- dr = Question Source: Rogawski 4e Calculus Early Transcendentais Publisher W.H. Freema 12 WG MacBook Proarrow_forwardEvaluate this integral using Green's Theorem c is described in figure belowarrow_forward
- Fast ,Show by Riemann integral theoryarrow_forwardSOLVE STEP BY STEP IN DIGITAL FORMAT Apply Green's theorem to obtain the result of the line integral - (7x²y — 4x)dy + (8xy³ − x²y ) dx - The integral starts at the origin so the value of y=0. Then it gets to the point (7,0) and moves to (7,4), so the value of x=7. Then it goes from the point (7,4) to the point (0,4) to the initial point (0,0), being in that last part x=0. That is, the limits of x will be from 0 to 7 and the limits of y will be from 0 to 4.arrow_forwardDirection: Using Riemann's Sum, find the integral of the following functions: 1.) √²(2x² - 5x + 1) dx 2.) √(x³- 2x + 1) dx 3.) f 2x³ dxarrow_forward
- Please show work. This is my calculus 3 hw. Part A onlyarrow_forwardEvaluate F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. IC S cos(x) sin(y) dx + sin(x) cos(y) dy 9 (371) 2 C: line segment from (0, -) to T 2arrow_forwardEvaluate the line integral by following the given steps. 2xy dx + 4x?y dy C is the triangle with vertices (0, 0),(3,0), and (0, 5). The curve C can split up into each one of its sides (shown in the picture below) H(t) L(t) B(t) $ 2ry dr + 4x?y dy 2xy dx + 4x?y dy + 2ry dx + 4x?y dy + 2ry da + 4x?y dy Parametrize each side of the triangle B(t) Σ te Σ Σ H(t) = Σ te Σ 1 Σ L(t) = Σ te Σ. Σ (use the most natural parametrizations and remember which direction you need to go) Express the line integral in terms of t 2ay dx + 4x?y dy 2ry dx + 4x?y dy + 2xy dx + 4x?y dy + 2xy dx + 4x?y dy Σ dt + E dt + Σdt .arrow_forward
- Calculus 3 Module: Line Integralarrow_forwardUsing the method of u-substitution, Se (6x - 8) dx = = [₁ f where U= du = a= b= f(u) = f(u) du (enter a function of x) da (enter a function of x) (enter a number) (enter a number) (enter a function of u). The value of the original integral is Note: You can earn full credit if the last answer box is correct and all other answer boxes are either blank or correct. Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. Email Instructorarrow_forwardHistory of mathematics Hippocrates’ Lunesarrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,
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