# Questions tagged [iterated-integrals]

This tag is for questions relating to iterated integrals. In calculus, an iterated integral is the result of applying integrals to a function of more than one variable (for example, $~f(x,y)~$ or $~f(x,y,z)~$) in a way that each of the integrals considers some of the variables as given constants.

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### Integral of $\int ^{5}_{1}\int ^{\sqrt{x-1}}_{y=0}{ye^{(x-1)^2}}dydx$

$\int ^{5}_{1}\int ^{\sqrt{x-1}}_{y=0}{ye^{(x-1)^2}}dydx$ First, I changed the integration from $x$ to $y$. However, I get $\int ^{5}_{1}\dfrac{\left( x-1\right) }{2}e^{\left( x-1\right) ^{2}}dx$ and ... 1 vote
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### Is this the correct integral for finding the volume of the region bounded by the planes $𝑧= 3𝑦,𝑧=𝑦,𝑦= 1,𝑥= 1,$ and $𝑥= 2$?

The integral I've formed here is: $$\int_1^2 \int_0^1 \int^{3y}_y 1 dzdydx$$ Which evaluates to one. Not sure if I'm thinking of the region correctly, does this integral make sense for this region? ...
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Problem: Solve the double integral $$I:=\int _{-\infty}^{\infty} \int _{-\infty}^{\infty} dx dy\ f(x,y),$$ where $f(x,y) = e^{-i a(x - y)}$ if $y > x$ and zero otherwise ($a$ is only a positive ...