Evaluating an Iterated Integral In Exercises 45-50, sketch the region of
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Calculus: Early Transcendental Functions
- Practice 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_forwardEvaluating 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_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
- Converting to a polar integral Integrate ƒ(x, y) = [ln (x2 + y2 ) ]/sqrt(x2 + y2) over the region 1<= x2 + y2<= e.arrow_forwardInstruction: Evaluate the following line integrals in the complex plane by direct integration (not using theorems)arrow_forwardTRANSFER TRAN SFER ACTIVITY 2: INTEGRATION THROUGH SUBSTITUTION Direction: Evaluate the following integrals. 1. S dx Vx 2. S dxarrow_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_forwardUsing the method of u-substitution, 5 [²(2x - 7)² de where U = du: = a = b = f(u) = = ·b [ f(u) du a It (enter a function of x) da (enter a function of ä) (enter a number) (enter a number) (enter a function of u). The value of the original integral is 9.arrow_forward4 sin(3y + a?)dydæ, a) Sketch the domain of integration on an (x,y)-plane. b) Set up the integral with the order of integration reversed. DO NOT EVALUATE THE INTEGRAL!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_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_forwarddx? What is the integrable form of 2 du du duarrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,