Changing the Order of
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- Finding u and du In Exercises 1–4, complete the table by identifying u and du for the integral. 1.. | F(9(x))/(x) dx u = g(x) du = g' (x) dx | (52? +1)*(10z) dæ | f(9(2))/(2) dæ 1 = g(x) du = g (x) dx 2 /æ³ +1 dx 3. | Fo(2))/ (x) dz = g(z) du = g (x) dæ tan? x sec? x dx 4. | f(g(x))g(x) dæ u = g(x) du = g (x) dx COs e sin? 2.arrow_forwardPractice with tabular integration Evaluate the following inte- grals using tabular integration (refer to Exercise 77). a. fre dx b. J7xe* de d. (x – 2x)sin 2r dx с. | 2r² – 3x - dx x² + 3x + 4 f. е. dx (x – 1)3 V2r + 1 g. Why doesn't tabular integration work well when applied to dx? Evaluate this integral using a different 1 x² method.arrow_forwardTRANSFER TRAN SFER ACTIVITY 2: INTEGRATION THROUGH SUBSTITUTION Direction: Evaluate the following integrals. 1. S dx Vx 2. S dxarrow_forward
- Converting to a polar integral Integrate ƒ(x, y) = [ln (x2 + y2 ) ]/sqrt(x2 + y2) over the region 1<= x2 + y2<= e.arrow_forwardChanging the order of integration Use another order of (4 (4z ( sin Vyz integration to evaluate I: dy dx dz.arrow_forwarde* What is the integrable form of dx? A du B du du D duarrow_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_forward2 2 2),-0 Exercises: Evaluate and Sketch the region of integration and write an equivalent double of integration reversed. 14-2x 1. dydx 0 2 2. [| dxdy 11-x 3. dyck 0 1-x 4. dydx 2 2x 5-| (4x+2)dydxarrow_forward(a) Sketch the region of integration R in the xy - plane and sketch the region G in the uv - plane using the coordinate transformation x = 2u and y = 2u + 4v.arrow_forward
- Using Integration by Parts In Exercises 11-14, find the indefinite integral using integration by parts with the given choices of u and dv. 11. x³ In x dx; u = In x, dv = x³ dx 12. (7 – x)ev² dx; u = 7 – x, dv = e² dx 13. + 1) sin 4x dx; u = 2x + 1, dv = sin 4x dx 14. cos 4x dx; u = x, dv = cos 4x dxarrow_forwardIntegrate using an appropriate integration technique. c) ⌠ [2,−2] dx/4 + x2arrow_forwardIntegrating with polar coordinates: Let Ω be a region in R2. Provide a double integral that represents the area of Ω when you integrate with polar coordinates.arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,