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- Using the fundamental theorem of calculus, find the area of the regions bounded by y=2 ,square root(x)-x, y=0arrow_forwardThe shaded area shown below is bounded by the line x = 3 m on the left, the x-axis on top, and the curve y = (-6x + x²) m on the right. 3 m 6 m y = (-6 x+ x) m -9 m Determine the coordinates of the centroid of the area in meters. X = E Earrow_forwardIntegrating with polar coordinates: Let Ω be a region in R2. Give a double integral that represents the area of Ω when you integrate with polar coordinates.arrow_forward
- Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the labeled regions are A1= 8, A2=4, A3=2 and A4=2 v= f(a)dx V= 10 A1 y=f(x) 3 A2 A3 A4 (figure is NOT to scale) 10arrow_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_forwardEvaluate the integral below by interpreting it in terms of areas in the figure. The areas of the labeled regions are A1-8, A2-4, A3=2 and A4=1 10 v=ff(z)dz V= A1 y=f(x) A2 5 A3 7 A4 (figure is NOT to scale) 10arrow_forward
- Using 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_forwardUsing polar coordinates, evaluate the integral (sin(x2+y2)dA) over the region 1<=x2+y2<=81.arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,