# Double integral [closed]

I am trying to use mathematica to verify a math problem which is a double integral: $$\int \int_D (3x+4)^4 \delta x\delta y$$ with $$0 \leq x \leq 4, 0 \leq y \leq 4,$$ I tried the following:

-drawing function:

f[x_, y_] := (3 x + 4 y)^4; R = ImplicitRegion[{0 < x < 4, 0 < y < 1}, {x, y}]; Plot3D[f[x, y], {x, y} \[Element] R]


And then writing a double integral in mathematica with the escape hotkey.

\!$$\*SubsuperscriptBox[\(\[Integral]$$, $$0$$, $$4$$]$$\*SubsuperscriptBox[\(\[Integral]$$, $$0$$, $$1$$]f[x,
y] \[DifferentialD]y \[DifferentialD]x\)\)


I tried as well:

Integrate[f[x, y], {x, 0, 4}, {y, o, 1}]


The first attempt gives me output 32, and the second gives me output:

-(512/5) (-374 + 162 o + 135 o^2 + 60 o^3 + 15 o^4 + 2 o^5)


## closed as off-topic by Lukas Lang, halirutan♦Jun 28 '18 at 11:41

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Lukas Lang, halirutan
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• You use o variable for y limits in second approach. That's the issue. – m0nhawk Jun 28 '18 at 7:40
• Shoot. Sorry about that. I changed the o to zero, but it does not give me a result still? – Dovendyr Jun 28 '18 at 8:31

I don't know what ...writing a double integral in mathematica with the escape hotkey means, but the three versions

Integrate[f[x, y], {x, 0, 4}, {y, 0, 1}]
Integrate[f[x, y], {x, y} \[Element] R]
\!$$\*SubsuperscriptBox[\(\[Integral]$$, $$0$$, $$4$$]$$\*SubsuperscriptBox[\(\[Integral]$$, $$0$$, $$1$$]f[x, y] \[DifferentialD]y \[DifferentialD]x\)\)
(*  191488/5 *)


give the same result!

• It's when you press escape, and write int, and then escape again :) – Dovendyr Jun 28 '18 at 12:29
• Can you please write how to plot it? I tried Plot3D, Plot3D[f[x, y], {x, y}] – Dovendyr Jun 28 '18 at 12:32
• Thanks. I prefer the click-version basic math input... – Ulrich Neumann Jun 28 '18 at 12:32
• Dovendyr@ Plot3D[f[x, y], {x, y} \[Element] R]  – Ulrich Neumann Jun 28 '18 at 12:35
• I'm missing the backslash "\" in your error message {x,y}[Element]R  , perhaps you forgot it in your plotcommand? – Ulrich Neumann Jun 28 '18 at 14:12

An overkill for this particular problem, but the technique is useful for more complicated regions:

Integrate[
f[x, y] Boole[0 < x < 4 && 0 < y < 1],
{x, -Infinity, Infinity}, {y, -Infinity, Infinity}]


$\frac{191488}{5}$