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Calculus (MindTap Course List)
- 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_forwardExistence. Integrate the function f(x, y) = 1/(1 - x²- y²) over the disk x²+ y² ≤ 3/4. Does the integral of f(x, y) exist over the disk x²+ y² ≤ 1? Justify your answer.arrow_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
- Evaluating Triple Iterated Integrals Evaluate the integrals in Exercises 7-20 1 cl cl 12. 0 J K x²+3x₂² Jo 2 3-3x-y o Jo 2 LI S ~ 0 2 → dx (x+y+z) dy dx dzarrow_forwardEvaluating Polar Integrals In Exercises 9-22, change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. μl pV²-3² 11 12. Jo Jo ra I √a²-x² тугилау dy dx JOJOarrow_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_forward
- calculus 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_forwardUsing the method of u-substitution, | (32 – 8)² dz = | f(u) du - where u = (enter a function of æ) du = da (enter a function of ¤) a = (enter a number) b = (enter a number) f(u) = (enter a function of u). The value of the original integral isarrow_forwardEvaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 5 y dx + 5 x²dy, where Cis the square with vertices (0, 0), (2, 0), (2, 2), and (0, 2) oriented counterclockwise. + iarrow_forward
- Determine the x- and y-coordinates of the centroid of the shaded area. y = 1+ -x - 1 2.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_forwardLine integrals Use Green’s Theorem to evaluate the following line integral. Assume all curves are oriented counterclockwise.A sketch is helpful. The flux line integral of F = ⟨ex - y, ey - x⟩, where C is theboundary of {(x, y): 0 ≤ y ≤ x, 0 ≤ x ≤ 1}arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,