Homework Answers
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6. (4 pts) Consider the double integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a) Sketch the region of integrationRin Figure 3.(b) By completing...
6. (4 pts) Consider the
double
integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a)
Sketch the region of integrationRin Figure 3.(b) By completing the
limits and integrand, set up (without evaluating) the integral in
polar coordinates.
-1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts) Consider the double integral V2 /2-y² + = (x2 + y) dx dy + + y) do dy. 2-y2 (a) Sketch the region of integration R in Figure 3. (b) By completing the limits and integrand, set up (without evaluating)...
6. (4 pts) Consider the double integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a) Sketch the region of integration R in Figure 3.(b)...
6. (4 pts) Consider the double
integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a)
Sketch the region of integration R in Figure 3.(b) By completing
the limits and integrand, set up (without evaluating) the integral
in polar coordinates.
2 1 2 X -2 FIGURE 3. Figure for Problem 6. 6. (4 pts) Consider the double integral V2 2-y2 (2? + y) dA= (32 + y) dx dy + (x2 + y) dx dy. 2-y? (a) ketch the region of integration R in Figure 3. (b) By completing...
6. (4 pts) Consider the double integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a) Sketch the region of integration R in Figure 3.(b)...
6. (4 pts) Consider the
double
integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a)
Sketch the region of integration R in Figure 3.(b) By completing
the limits and integrand, set up (without evaluating) the integral
in polar coordinates.∫R(x2+y)dA=∫∫drdθ.7. (5 pts) By completing the
limits and integrand, set up (without evaluating) an iterated
inte-gral which represents the volume of the ice cream cone bounded
by the cone z=√x2+y2andthe hemisphere z=√8−x2−y2using(a) Cartesian
coordinates.volume =∫∫∫dz dxdy.(b) polar coordinates.volume
=∫∫drdθ.
-1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts)...
The region R is bounded by the x-axis and y = V16 – x2 a) Sketch...
The region R is bounded by the x-axis and y = V16 – x2 a) Sketch the bounded region R. Label your graph. b) Set up the iterated integral to solve for the area of the bounded region using either the Rx region or Ry region. Do not integrate. Evaluate the integral using polar coordinates for the region R. sec(x2 + y2) tan(x2 + y2) da c) R
2) The region R is bounded by the x-axis and y = V16 - x2 a)...
2) The region R is bounded by the x-axis and y = V16 - x2 a) (0.75 point) Sketch the bounded region R. Label your graph. b) (0.75 point) Set up the iterated integral to solve for the area of the bounded region using either the Ry region or Ry region. Do not integrate. c) (1.25 point) Evaluate the integral using polar coordinates for the region R. sec(x2 + y2) tan(x2 + y2) dA R
2) The region R is bounded by the x-axis and y = V16 - x2 a)...
2) The region R is bounded by the x-axis and y = V16 - x2 a) (0.75 point) Sketch the bounded region R. Label your graph. b) (0.75 point) Set up the iterated integral to solve for the area of the bounded region using either the Rx region or Ry region. Do not integrate. c) (1.25 point) Evaluate the integral using polar coordinates for the region R. sec(x2 + y2) tan(x2 + y2) dA R
2) The region R is bounded by the x-axis and y = V16 – x2. a)...
2) The region R is bounded by the x-axis and y = V16 – x2. a) (0.75 point) Sketch the bounded region R. Label your graph. b) (0.75 point) Set up the iterated integral to solve for the area of the bounded region using either the Rx region or Ry region. Do not integrate. c) (1.25 point) Evaluate the integral using polar coordinates for the region R. S sec(x2 + y2) tan(x2 + y2) da R
2) The region R is bounded by the x-axis and y = V16 – x2 a)...
2) The region R is bounded by the x-axis and y = V16 – x2 a) (0.75 point) Sketch the bounded region R. Label your graph. b) (0.75 point) Set up the iterated integral to solve for the area of the bounded region using either the Rx region or Ry region. Do not integrate. c) (1.25 point) Evaluate the integral using polar coordinates for the region R. S sec(x2 + y2) tan(x2 + y2) da R
1 -1 O 1 2 x FIGURE 3. Figure for Problem 6. 6. (4 pts) Consider...
1 -1 O 1 2 x FIGURE 3. Figure for Problem 6. 6. (4 pts) Consider the double integral 2 Spa (22 + y)da = [ L. (x2 + y) dx dy + √2-y² (x2 + y) dx dy. (a) Sketch the region of integration R in Figure 3. (b) By completing the limits and integrand, set up (without evaluating) the integral in polar coordinates. Sep (+2 +y)dA = dr do.
Q#2 Sketch the region of integration and use polar coordinates to find the value of the...
Q#2 Sketch the region of integration and use polar coordinates to find the value of the integral : a Va2-x2 r?+y2 1+(x2+y232 dy dr. 0 -Na2-x2
6. (4 pts) Consider the
double
integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a)
Sketch the region of integrationRin Figure 3.(b) By completing the
limits and integrand, set up (without evaluating) the integral in
polar coordinates.
-1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts) Consider the double integral V2 /2-y² + = (x2 + y) dx dy + + y) do dy. 2-y2 (a) Sketch the region of integration R in Figure 3. (b) By completing the limits and integrand, set up (without evaluating)...
6. (4 pts) Consider the double
integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a)
Sketch the region of integration R in Figure 3.(b) By completing
the limits and integrand, set up (without evaluating) the integral
in polar coordinates.
2 1 2 X -2 FIGURE 3. Figure for Problem 6. 6. (4 pts) Consider the double integral V2 2-y2 (2? + y) dA= (32 + y) dx dy + (x2 + y) dx dy. 2-y? (a) ketch the region of integration R in Figure 3. (b) By completing...
6. (4 pts) Consider the
double
integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a)
Sketch the region of integration R in Figure 3.(b) By completing
the limits and integrand, set up (without evaluating) the integral
in polar coordinates.∫R(x2+y)dA=∫∫drdθ.7. (5 pts) By completing the
limits and integrand, set up (without evaluating) an iterated
inte-gral which represents the volume of the ice cream cone bounded
by the cone z=√x2+y2andthe hemisphere z=√8−x2−y2using(a) Cartesian
coordinates.volume =∫∫∫dz dxdy.(b) polar coordinates.volume
=∫∫drdθ.
-1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts)...
The region R is bounded by the x-axis and y = V16 – x2 a) Sketch the bounded region R. Label your graph. b) Set up the iterated integral to solve for the area of the bounded region using either the Rx region or Ry region. Do not integrate. Evaluate the integral using polar coordinates for the region R. sec(x2 + y2) tan(x2 + y2) da c) R
2) The region R is bounded by the x-axis and y = V16 - x2 a) (0.75 point) Sketch the bounded region R. Label your graph. b) (0.75 point) Set up the iterated integral to solve for the area of the bounded region using either the Ry region or Ry region. Do not integrate. c) (1.25 point) Evaluate the integral using polar coordinates for the region R. sec(x2 + y2) tan(x2 + y2) dA R
2) The region R is bounded by the x-axis and y = V16 - x2 a) (0.75 point) Sketch the bounded region R. Label your graph. b) (0.75 point) Set up the iterated integral to solve for the area of the bounded region using either the Rx region or Ry region. Do not integrate. c) (1.25 point) Evaluate the integral using polar coordinates for the region R. sec(x2 + y2) tan(x2 + y2) dA R
2) The region R is bounded by the x-axis and y = V16 – x2. a) (0.75 point) Sketch the bounded region R. Label your graph. b) (0.75 point) Set up the iterated integral to solve for the area of the bounded region using either the Rx region or Ry region. Do not integrate. c) (1.25 point) Evaluate the integral using polar coordinates for the region R. S sec(x2 + y2) tan(x2 + y2) da R
2) The region R is bounded by the x-axis and y = V16 – x2 a) (0.75 point) Sketch the bounded region R. Label your graph. b) (0.75 point) Set up the iterated integral to solve for the area of the bounded region using either the Rx region or Ry region. Do not integrate. c) (1.25 point) Evaluate the integral using polar coordinates for the region R. S sec(x2 + y2) tan(x2 + y2) da R
1 -1 O 1 2 x FIGURE 3. Figure for Problem 6. 6. (4 pts) Consider the double integral 2 Spa (22 + y)da = [ L. (x2 + y) dx dy + √2-y² (x2 + y) dx dy. (a) Sketch the region of integration R in Figure 3. (b) By completing the limits and integrand, set up (without evaluating) the integral in polar coordinates. Sep (+2 +y)dA = dr do.
Q#2 Sketch the region of integration and use polar coordinates to find the value of the integral : a Va2-x2 r?+y2 1+(x2+y232 dy dr. 0 -Na2-x2
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