Calculation Of First Moment February 6

I'd like to calculate the following: $$ \int y\partial_{y_2} [(y_1+y_2)p(y)] dy,$$ where $p$ is a probability density and $y=(y_1,y_2,y_3)$ is a vector.I need integration by parts here so I need the integral$$ \int \partial_{y_2} [(y_1+y_2)p(y)] dy.$

Calculate the mass of K February 6    2

Calculate the mass of K
The curves $y = \cos x$ , $y = \sin 2 x$ and the y-axis defines the flat figure K.K's density in the point (x,y) is $\cos x$ mass units per area unit.Calculate the mass of K.I stated the den ...

Finding the area under a speed time graph February 6    1

Finding the area under a speed time graph
I recently learned about integration and I wondered how it could be applied to a speed time graph since it does not have a particular equation of a line that one can integrate. Do you split ...

Integration that results to give bessels function February 6

I have to integrate the following :$$\int_0^\infty x^{s-1}e^{(-ax^p-bx^{-q})}dx$$Please help me I am not able to solve this .. However there is this identity available in a book $$\int_0^\infty x^{s-1}e^{(-ax^p-bx^{-p})}dx = 2 p^{-1}(\frac{b}{a})^{(\

Fining the angular bounds of a triple integral function February 6

Fining the angular bounds of a triple integral function
This problem requires the taking of a triple integral over a region. I believe it's most useful to convert to cylindrical coordinates, which I did. However, I could not find the theta bounds ...

Can limits to definite integral be vectors February 6

There are two cases: 1-Limits are scalar and function to be integrated is vector.2- Limits are vector and function to be integrated is vector.Are both valid. If yes can you give example for each.Actually the problem is I have problem in which I have

How to prove Integral result February 6    1

How to prove Integral result
I am trying to solve a integral through Mathematica, Mathematica gives me the following answer My question is how to solve this integral manually to get the Mathematica result or can we prov ...

Angular Velocity through integration February 6    1

How to integrate $a\ddot\theta = \frac{gsin2\theta}{2} $ to find $r\dot\theta^2$r is the radius. I am not sure how to integrate the equation with respect to t. Kindly explain.Start with $$\ddot\theta = \frac g {2a} \sin(2\theta)$$and multiply both si

Proving the problem of integration February 6    2

From a journal, they proved this equality:$$ \frac{z}{\alpha -1}\left(\int_0^1 \frac{t^{\frac{1}{\alpha}}}{1-tz} dt -\alpha \int_0^1 \frac{v}{1-vz} dv\right) = \int_0^1 t^{\frac{1}{\alpha}} \left(\int_0^1 \frac{vz}{1-tvz}dv\right)dt $$I already tried

integral of $\ln x$ from 0 to 1 February 6    2

I have a question about the integral of $\ln x$.When I try to calculate the integral of $\ln x$ from 0 to 1 I always get the following result.$x(\ln x -1)$ (integral of $\ln x$)$1(\ln 1 -1) - (0 (\ln 0 -1))$ But the second part of the calculation is

Reverse Power Rule integration. February 6    2

Ok, so I am confused about the following;When we have a polynomial, say $P(x)$, and we want to solve an integral where $P(x)$ is raised to a certain power, for example; $$\int (P(x))^adx$$Why can we not integrate it using the fact that integration is

You Might Also Like