Scalar line
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Calculus: Early Transcendentals (2nd Edition)
- 5. Prove that the equation has no solution in an ordered integral domain.arrow_forwardFind the area between the curves in Exercises 1-28. x=0, x=/4, y=sec2x, y=sin2xarrow_forward2ni 2n+i 1 (b) / (c) / (d) / (iz – 1)³ dz. 3. Evaluate the integrals: (a) sinh z dz, cos 3z dz, e*z dz, - T-i 23 + 3 4. Evaluate the integral P 2 + 3z – 10 dz, where C is the circle (a) |z + 3| = 3, (b) |2| = 3, (c) |z| = 7. dz 5. Evaluate the integral where C is the circle (a) |z| = 1, (b) |z+ 3| = 2, (c) |z – 3| = 2. 23(z – 4)' Carrow_forward
- WHite the veD secsand orde equation as is equivalent svstem of hirst order equations. u" +7.5z - 3.5u = -4 sin(3t), u(1) = -8, u'(1) -6.5 Use v to represent the "velocity fumerion", ie.v =(). Use o and u for the rwo functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.) +7.5v+3.5u-4 sin 3t Now write the system using matrices: dt 3.5 7.5 4 sin(3t) and the initial value for the vector valued function is: u(1) v(1) 3.5arrow_forwardFind div F and curl F if F(x, y, z) = 10e i − 4 cos y j + sin² z k. div F= curl F=arrow_forwarda) Evaluate y? dydx. b) Evaluate the line integral Cos x cos y dx + (1 – sin x sin y) dy - where C is the part of the curve y = sin x from x = 0 to x = T/2.arrow_forward
- Set up, but do not evaluate, an integral that represents the length of the parametric curve Select the correct answer. 10 2x O√₁ +3² (In 3)² dx 5 10 O√T 1 + 3* In 3 dx 5 5 O √1 +3² (In 3)² dx J 10 10 Of 3²* (In 3)² dx 5 √1 + 10² (In 10)² dx y=3*, 5 ≤ x ≤ 10.arrow_forwarda) Evaluate the integrals using appropriate substitutions. dx Sino i) S de u) I Cos?8+ 1 ü) j 1+16x2 b) Evaluate the integrals using Part 1 of the Fundamental Theorem of Calculus. /2(x+ 2 L 4x(1 – x?)dx ii) (x + -) dx Sin2x i) c) Use Part 2 of the Fundamental Theorem of Calculus to find the derivatives. evE dt d d i) ii) Intdt dx dxarrow_forwardShow that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals to find its value. NOTE: Enter the exact answer. r(5,7) 2xe dx + x*edy (0,0)arrow_forward
- Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 4 ydx + 3 x²dy, where Cis the square with vertices (0,0), (1, 0), (1, 1), and (0, 1) oriented counterclockwise. 643° dx + 3 x°dy = iarrow_forwardEvaluate F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. (3yi + 3xj) · dr C: smooth curve from (0, 0) to (3, 2)arrow_forwardUse Green's Theorem to evaluate the line integral. Lex cos(2y) dx – 2ex sin(2y) dy C: x2 + y2 = a²arrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,