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sleet_krkn [62]
3 years ago
14

Evaluate the double integral ∬Ry2x2+y2dA, where R is the region that lies between the circles x2+y2=16 and x2+y2=121, by changin

g to polar coordinates.

Mathematics
1 answer:
olga2289 [7]3 years ago
8 0

Answer:

See answer and graph below

Step-by-step explanation:

∬Ry2x2+y2dA

=∫Ry.2x.2+y.2dA

=A(2y+4Ryx)+c

=∫Ry.2x.2+y.2dA

Integral of a constant ∫pdx=px

=(2x+2.2Ryx)A

=A(2y+4Ryx)

=A(2y+4Ryx)+c

The graph of y=A(2y+4Ryx)+c assuming A=1 and c=2

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Answer:

see explanation

Step-by-step explanation:

Find the coordinates of c using the section formula

x_{c} = \frac{(3(1)+(2(6)}{2+3} = \frac{3+12}{5} = 3

y_{c} = \frac{(3(4))+(2(-1))}{2+3} = \frac{12-2}{5} = 2

coordinates of c = (3, 2)

Similarly to find the coordinates of d

x_{d} = \frac{x(2(1))+(3(3))}{3+2} = \frac{2+9}{5} = \frac{11}{5}

y_{d} = \frac{(2(4))+(3(2))}{3+2} = \frac{8+6}{5} = \frac{14}{5}

coordinates of d = ( \frac{11}{5}, \frac{14}{5})


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Step-by-step explanation:

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quarters:  x

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