Simple Strategies for Solving Problems to Effective Solutions

[Superposed_Cat]

How would you go about solving this?

 

[arildno]

Integrate it?
Where is your specific problem?

 

[UltrafastPED]

It's a triple integral (a volume, for example). You need two more sets of integration limits. Since one of the integration variables doesn't appear in the integrand you can integrate it directly - it would most likely end up as a factor of 2pi. Looking at the remaining parts, you can integrate each separately, taking into account the integration limits.

 

[TysonM8]

c∫d α∫β 1∫2 ρ^2 sin∅ dρd∅dθ

= c∫d α∫β [(ρ^3)/3 sin∅] [1,2] d∅dθ
= c∫d α∫β 7/3 sin∅ d∅dθ
= c∫d [-7/3 cos∅] [α,β] dθ
= c∫d [-7/3 cosβ] - [-7/3 cosα] dθ
= c∫d 7/3 (cosα - cosβ) dθ
= [(7θ)/3 (cosα - cosβ)] [c,d]
= [(7d)/3 (cosα - cosβ)] - [(7c)/3 (cosα - cosβ)]
= (1/3)(7d-7c)(cosα - cosβ)

This is the general solution where α≤∅≤β and c≤∅≤d

 

[Superposed_Cat]

Sorry, cropped too much there.

 

[HallsofIvy]

That's easy then! Since the limits of integraton are all constants and the integrand is just a product of functions of the separate variables, that is just
$$\left(\int_1^2 \rho^2 d\rho\right)\left(\int_{\pi/2}^\pi \sin(\phi) d\phi\right)\left(\int_0^2 d\theta\right)$$

Though I must say the limits of integration on that last, $d\phi$, integral look suspicious to me! It's not impossble- but "0 to 2 radians" seems peculiar. "0 to $2\pi$" would see much more reasonable. That would be integrating over a hemi-spherical "cup", below the xy-plane with thickness from 1 to 2.

 

[Superposed_Cat]

Why is that weird?

 

[Crake]

c∫d α∫β 1∫2 ρ^2 sin∅ dρd∅dθ

= c∫d α∫β [(ρ^3)/3 sin∅] [1,2] d∅dθ
= c∫d α∫β 7/3 sin∅ d∅dθ
= c∫d [-7/3 cos∅] [α,β] dθ
= c∫d [-7/3 cosβ] - [-7/3 cosα] dθ
= c∫d 7/3 (cosα - cosβ) dθ
= [(7θ)/3 (cosα - cosβ)] [c,d]
= [(7d)/3 (cosα - cosβ)] - [(7c)/3 (cosα - cosβ)]
= (1/3)(7d-7c)(cosα - cosβ)

This is the general solution where α≤∅≤β and c≤∅≤d

Dude, you should seriously learn latex! It's not that hard and it makes it so much easier for everyone to read what you write. It also looks way better and it's probably better for you as well!

Just take a look at this link.

 

[Crake]

Why is that weird?

You're integrating using spherical coordinates. $\theta$ is an angle and it seems weird that it goes from $0$ to $2$ radians.