Integrate 0 1 √1-x² √1-x²-y² 0 0 sin (√√z² + y² + x²) 3 (z² + y² + x²) dz dy dx. Give the answer in its exact form. This will include either a sine or a cosine function. The value of the integral is If 0 ≤ z ≤ √√√1 - x² - y² then in a spherical coordinate system (x, y, z) → (p cos 0 sin , p sin 0 sin , p cos ) we have that 0 ≤ ≤ π/2.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
Integrate
1 v
2_2
I T
0 0
sin (√ z² + y² + x²)
3 (z² + y² + x²)
2
dz dy dx.
Give the answer in its exact form. This will include either a sine or a cosine function.
The value of the integral is
If 0 ≤ z ≤ √ 1 − x² y² then in a spherical coordinate system (x, y, z) → (p cos 0 sin , p sin sin , pcos ) we have that 0 ≤ ¢ ≤ π/2.
Transcribed Image Text:Integrate 1 v 2_2 I T 0 0 sin (√ z² + y² + x²) 3 (z² + y² + x²) 2 dz dy dx. Give the answer in its exact form. This will include either a sine or a cosine function. The value of the integral is If 0 ≤ z ≤ √ 1 − x² y² then in a spherical coordinate system (x, y, z) → (p cos 0 sin , p sin sin , pcos ) we have that 0 ≤ ¢ ≤ π/2.
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