VT/2y cos (x) dr dyT/Evaluate

Name: VT/2y cos (x) dr dyT/Evaluate
Uploaded: 2024-03-20T06:47:22.000Z
Channel: Bartleby
Description: VT/2y cos (x) dr dyT/Evaluate

We have the given double integration is ∫0π23∫yπ23ycos(x3)dxdy Here the integration is done first…

Answered: Evaluate y cos (r*) dr dy

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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We have the given double integration is $\int_{0}^{\sqrt[3]{\frac{π}{2}}} \int_{y}^{\sqrt[3]{\frac{π}{2}}} y \cos (x^{3}) d x d y$

Here the integration is done first with respect to x.

Now, to evaluate the above integral we change the order of integration.

Here x changes from $x = y t o x = \sqrt[3]{\frac{π}{2}}$ and y changes from $y = 0 t o \sqrt[3]{\frac{π}{2}}$

After changing order of integration y changes from y=0 to y=x and x changes from $x = 0 t o \sqrt[3]{\frac{π}{2}}$

So, the above integral transform into

$\int_{y = 0}^{\sqrt[3]{\frac{π}{2}}} \int_{x = y}^{\sqrt[3]{\frac{π}{2}}} y \cos (x^{3}) d x d y = \int_{x = 0}^{\sqrt[3]{\frac{π}{2}}} \int_{y = 0}^{x} y \cos (x^{3}) d x d y$

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