Evaluating an Iterated Integral In Exercises 45-50, sketch the region of
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Calculus: Early Transcendental Functions
- Evaluating Triple Iterated Integrals Evaluate the integrals in Exercises 7-20 10. $1 S S 0 JO cl ✓x²+3y² 3-3x 3-3x-y clc2 JU 0 dy dz dy dx du drarrow_forwardFinding 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_forward
- Showing all work, Evaluate: ∫4∞[(dt)/(t3/2)]arrow_forwardFind the area between the curves in Exercises 1-28. x=2, x=1, y=2x2+5, y=0arrow_forwardcalculus 2_homework2_updated 16. Let B be the region in the first quadrant of the xy-plane bounded by the lines r + y = 1, x + y = 2, (x – y)² x = 0 and y = 0. Evaluate dædy by applying the transformation u = x + y, v = x – y 1+x + y Barrow_forward
- Determine the x- and y-coordinates of the centroid of the shaded area. y = 1+ -x - 1 2.arrow_forwardQUICK CHECK 3 Let u(t) = (t,t, t) and v(t) = (1, 1, 1). Compute d (n(t) • v(t)) using Derivative dt Rule 5, and show that it agrees with the result obtained by first computing the dot product and differentiating directly. <arrow_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
- сп show that f(x=3x is integralble [0,4] using the definition.arrow_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_forwardUsing 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_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,