Convert the following to rectangular coordinates and spherical coordinates. Do not evaluate the integral. c2π 4-² √1²= [V²] [✓²*² T r²0 dz dr de

Q: cos" x sin xdx

A: We need to evaluate the following integral I = ∫cos7x sinx dx…

Q: = M I = √√3-1² S₂3 2 √2-√√4-1²-y² 2y dz dy dr

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Q: Evaluate the given integral by making an appropriate change of variables. 11. dA, where R is the…

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Q: sososo 0 0 √x² + y² dy dx dz

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Q: Convert the following integrals to polar first and then www www wwwwww calculate. 9-y2 ydxdy xdydx…

A: Use  ,  and   to convert Cartesian form to polar form . Note : The area can represented by .

Q: Evaluate the integral by changing to spherical coordinates. (x³ + xy² + æz²) dz dy dæ

A: The limits of integration are  -1-x2-y2≤z≤1-x2-y2, 0≤y≤1-x2 and -1≤x≤0 It is one-fourth of the unit…

Q: Evaluate the following iterated integral by converting to polar coordinates. 49-x2 ydydx

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Q: -√3 -².² -√3 Jo I = 3-1 1²+y² 2-√√/4-1²-y² 2y dz dy dr

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Q: Graph the integrand and use geometry to evaluate the integral. 6 2) s V36 - x2 dx -6

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Q: Write the x and y coordinates of any point on the unit circle in terms of the angle theta…

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Q: Evaluate the integral by converting to polar coordinates. 1 de dy = V1+x² + y²

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Q: Consider the following. A = Convert the iterated integral to polar coordinates. A B S^L. ( Jo Jo B =…

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Q: Convert the double integral (∫0 to 2π ∫1 to 2 (cos θ − sin θ)r dr dθ) to rectangular coordinates

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Q: Evaluate the given integral by changing to polar coordinates. 13

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