How do I go about finding the double integral in first quadrant, given $y=x^2$ and $y=x^3$?I can't figure out how to solve the polar integral for finding the area!How do I go about solving the integral of csc x?Change of variables in a double integral - how to find the region??Integrating an area bounded by three lines/curvesA double integral question about finding volume of a segment of cylinderEvaluate the integral that gives the area in the first quadrant between the circlesFinding when a double integral is convergentCalculating the area with simple and double integralsUsing a triple integral to find the volume of a solid bounded by $y=0, ;; z=0, ;; y=x, ;; and ;;z=4-x^2-y^2$ in the first octant.The area under the curve 1/x in the first quadrant (integral)
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How do I go about finding the double integral in first quadrant, given $y=x^2$ and $y=x^3$?
I can't figure out how to solve the polar integral for finding the area!How do I go about solving the integral of csc x?Change of variables in a double integral - how to find the region??Integrating an area bounded by three lines/curvesA double integral question about finding volume of a segment of cylinderEvaluate the integral that gives the area in the first quadrant between the circlesFinding when a double integral is convergentCalculating the area with simple and double integralsUsing a triple integral to find the volume of a solid bounded by $y=0, ;; z=0, ;; y=x, ;; and ;;z=4-x^2-y^2$ in the first octant.The area under the curve 1/x in the first quadrant (integral)
$begingroup$
"$$iint_R 2xy, dA$$ where $R$ is the limited area in the first quadrant between the graphs $y = x^2$ and $y = x^3$"
How do I find the $R$ values I'm lacking from the given information? I understand I should somehow use these y values to find the rest of the $R$, but I have no idea how, and would appreciate any help I can get.
Thanks in advance! :)
calculus integration
edited Mar 29 at 21:54
Minus One-Twelfth
3,328413
asked Mar 29 at 21:39
BetelgeuseBetelgeuse
31
$endgroup$
add a comment |
$begingroup$
"$$iint_R 2xy, dA$$ where $R$ is the limited area in the first quadrant between the graphs $y = x^2$ and $y = x^3$"
How do I find the $R$ values I'm lacking from the given information? I understand I should somehow use these y values to find the rest of the $R$, but I have no idea how, and would appreciate any help I can get.
Thanks in advance! :)
calculus integration
edited Mar 29 at 21:54
Minus One-Twelfth
3,328413
asked Mar 29 at 21:39
BetelgeuseBetelgeuse
31
$endgroup$
$begingroup$
Suppose this was a question in first year calculus, find the area of region R. What does this integral look like? This will hopefully give you some insight into the bounds for R in this double integral.
$endgroup$
– Doug M
Mar 29 at 21:41
add a comment |
$begingroup$
"$$iint_R 2xy, dA$$ where $R$ is the limited area in the first quadrant between the graphs $y = x^2$ and $y = x^3$"
How do I find the $R$ values I'm lacking from the given information? I understand I should somehow use these y values to find the rest of the $R$, but I have no idea how, and would appreciate any help I can get.
Thanks in advance! :)
calculus integration
edited Mar 29 at 21:54
Minus One-Twelfth
3,328413
asked Mar 29 at 21:39
BetelgeuseBetelgeuse
31
$endgroup$
"$$iint_R 2xy, dA$$ where $R$ is the limited area in the first quadrant between the graphs $y = x^2$ and $y = x^3$"
How do I find the $R$ values I'm lacking from the given information? I understand I should somehow use these y values to find the rest of the $R$, but I have no idea how, and would appreciate any help I can get.
Thanks in advance! :)
calculus integration
calculus integration
edited Mar 29 at 21:54
Minus One-Twelfth
3,328413
asked Mar 29 at 21:39
BetelgeuseBetelgeuse
31
edited Mar 29 at 21:54
Minus One-Twelfth
3,328413
asked Mar 29 at 21:39
BetelgeuseBetelgeuse
31
edited Mar 29 at 21:54
Minus One-Twelfth
3,328413
edited Mar 29 at 21:54
Minus One-Twelfth
3,328413
edited Mar 29 at 21:54
Minus One-Twelfth
3,328413
3,328413
asked Mar 29 at 21:39
BetelgeuseBetelgeuse
31
asked Mar 29 at 21:39
BetelgeuseBetelgeuse
31
asked Mar 29 at 21:39
BetelgeuseBetelgeuse
31
31
$begingroup$
Suppose this was a question in first year calculus, find the area of region R. What does this integral look like? This will hopefully give you some insight into the bounds for R in this double integral.
$endgroup$
– Doug M
Mar 29 at 21:41
add a comment |
$begingroup$
Suppose this was a question in first year calculus, find the area of region R. What does this integral look like? This will hopefully give you some insight into the bounds for R in this double integral.
$endgroup$
– Doug M
Mar 29 at 21:41
$begingroup$
Suppose this was a question in first year calculus, find the area of region R. What does this integral look like? This will hopefully give you some insight into the bounds for R in this double integral.
$endgroup$
– Doug M
Mar 29 at 21:41
$begingroup$
Suppose this was a question in first year calculus, find the area of region R. What does this integral look like? This will hopefully give you some insight into the bounds for R in this double integral.
$endgroup$
– Doug M
Mar 29 at 21:41
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
If we have $x^3le yle x^2$ then the only points in which the bounding graphs intersect are when $x^3=x^2implies x=0,1$. So the bounds for $x$ must be $0le xle1$ in order for a finite region to be bounded. So, the integral is given by
$$intint_R 2xy dA=int_0^1int_x^3^x^22xydydx$$
Then the integral is equal to
$$int_0^1int_x^3^x^22xydydx=int_0^1xcdot[y^2]_x^3^x^2dx=int_0^1x^5-x^7dx=[frac16x^6-frac18x^8]_0^1=frac124$$
answered Mar 29 at 21:52
Peter ForemanPeter Foreman
6,2261317
$endgroup$
add a comment |
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1 Answer
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1 Answer
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$begingroup$
If we have $x^3le yle x^2$ then the only points in which the bounding graphs intersect are when $x^3=x^2implies x=0,1$. So the bounds for $x$ must be $0le xle1$ in order for a finite region to be bounded. So, the integral is given by
$$intint_R 2xy dA=int_0^1int_x^3^x^22xydydx$$
Then the integral is equal to
$$int_0^1int_x^3^x^22xydydx=int_0^1xcdot[y^2]_x^3^x^2dx=int_0^1x^5-x^7dx=[frac16x^6-frac18x^8]_0^1=frac124$$
answered Mar 29 at 21:52
Peter ForemanPeter Foreman
6,2261317
$endgroup$
add a comment |
$begingroup$
If we have $x^3le yle x^2$ then the only points in which the bounding graphs intersect are when $x^3=x^2implies x=0,1$. So the bounds for $x$ must be $0le xle1$ in order for a finite region to be bounded. So, the integral is given by
$$intint_R 2xy dA=int_0^1int_x^3^x^22xydydx$$
Then the integral is equal to
$$int_0^1int_x^3^x^22xydydx=int_0^1xcdot[y^2]_x^3^x^2dx=int_0^1x^5-x^7dx=[frac16x^6-frac18x^8]_0^1=frac124$$
answered Mar 29 at 21:52
Peter ForemanPeter Foreman
6,2261317
$endgroup$
add a comment |
$begingroup$
If we have $x^3le yle x^2$ then the only points in which the bounding graphs intersect are when $x^3=x^2implies x=0,1$. So the bounds for $x$ must be $0le xle1$ in order for a finite region to be bounded. So, the integral is given by
$$intint_R 2xy dA=int_0^1int_x^3^x^22xydydx$$
Then the integral is equal to
$$int_0^1int_x^3^x^22xydydx=int_0^1xcdot[y^2]_x^3^x^2dx=int_0^1x^5-x^7dx=[frac16x^6-frac18x^8]_0^1=frac124$$
answered Mar 29 at 21:52
Peter ForemanPeter Foreman
6,2261317
$endgroup$
If we have $x^3le yle x^2$ then the only points in which the bounding graphs intersect are when $x^3=x^2implies x=0,1$. So the bounds for $x$ must be $0le xle1$ in order for a finite region to be bounded. So, the integral is given by
$$intint_R 2xy dA=int_0^1int_x^3^x^22xydydx$$
Then the integral is equal to
$$int_0^1int_x^3^x^22xydydx=int_0^1xcdot[y^2]_x^3^x^2dx=int_0^1x^5-x^7dx=[frac16x^6-frac18x^8]_0^1=frac124$$
answered Mar 29 at 21:52
Peter ForemanPeter Foreman
6,2261317
answered Mar 29 at 21:52
Peter ForemanPeter Foreman
6,2261317
answered Mar 29 at 21:52
Peter ForemanPeter Foreman
6,2261317
answered Mar 29 at 21:52
Peter ForemanPeter Foreman
6,2261317
6,2261317
add a comment |
add a comment |
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$begingroup$
Suppose this was a question in first year calculus, find the area of region R. What does this integral look like? This will hopefully give you some insight into the bounds for R in this double integral.
$endgroup$
– Doug M
Mar 29 at 21:41