Evaluate the double integral. (x2 y)dxdy 5. 6. Use (repeated) integration by parts to find 4x cos 2xdx.
Evaluate the double integral. (x2 y)dxdy 5. 6. Use (repeated) integration by parts to find 4x cos 2xdx.
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)...
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)...
Evaluate the iterated integral Sa Wa?-? (x2 + y2); dxdy that is given in cartesian coordinates by converting to polar coordinates.
Q.6) Suppose that B is the set defined as B = {(x,y) y 20 and x2 + y2 S 4}. Evaluate the integral ľs V.x2 + y? dxdy using change of variables. (20 Pts.)
Q.6) Suppose that B is the set defined as B = {(x,y) y 20 and x2 + y2 4}. Evaluate the integral si 1x2 + y2 dxdy using change of variables. (20 pts.)
Required information Consider the following double integral. $ 14 (x2 – 6y2 + xy3 )dxdy Evaluate the double integral using single applications of Simpson's 1 / 3 rule. Also, compute the percent relative error. (Round the final answers to three decimal places.) The solution of the double integral is True percent relative error is %.
Area between the curve problems
1. Find the area between y 1/x, y 1/x2 and x 2 2. Find the area between y 8-x2, y x2, x -3 and 3. 3. Find (approximately) the area between y r cos (2) and y
1. Find the area between y 1/x, y 1/x2 and x 2 2. Find the area between y 8-x2, y x2, x -3 and 3. 3. Find (approximately) the area between y r cos (2) and y
Evaluate, 23:58 2 x 2 + y dxdy by converting to polar coordinates.