4. This problem is concerned with the Gaussian or Bell curve.(a) Let D be a disk centered on the origin of radius R. CalculateJe-e¯(z²+y²) dA.(b) Determine the value when R→∞o. Which improper integral in Cartesian coordinates does thiscorrespond to?(c) Explain why(d) Use these results to show that[*[*e-²³+3³) dy dx = (* ²³ dx) ([^e²² dy).eсaсLe-²-1²dx =√R.

The given integral is , where is a disk centered at origin of radius .We need to prove that .

This problem is concerned with the Gaussian or Bell cur curve. (a) Let D be a disk centered on the origin of radius R. Calculate √√₁₂ e-(2²+1³²) (b) Determine the value when R→ ∞. Which improper integral in Cartesian coordinates does this correspond to? (c) Explain why d.A. [° [² =−(²+5¹) dy dz = ([^~^²³ dz) ([ªc-³² dy). e-2² P (d) Use these results to show that dx = √R.

This problem is concerned with the Gaussian or Bell cur curve. (a) Let D be a disk centered on the origin of radius R. Calculate √√₁₂ e-(2²+1³²) (b) Determine the value when R→ ∞. Which improper integral in Cartesian coordinates does this correspond to? (c) Explain why d.A. [° [² =−(²+5¹) dy dz = ([^~^²³ dz) ([ªc-³² dy). e-2² P (d) Use these results to show that dx = √R.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.3: Implicit Differentiation

Problem 42E

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