Question

Help please..
Beta function

Answer 1

\[\int\limits\limits_{0}^{\pi}x\cdot \cos^6x\cdot \sin^5xdx \]

Answer 2

The adjacency matrix L encodes the graph. The entry Lij is equal to k if there are k connections between node i and j. Otherwise, the entry is zero. Problem 2 asks to find the matrix which encodes all possible paths of length 3. Generating function. To a graph one can assign for pair of nodes i,j a series f(z) = \sum_{n=0}^{\infty} a_n^(ij) zⁿ, where an(ij) is the number of walks from i to j with n steps. Problem 3) asks for a formula for f(z) and in problem 4) an explicit expression in the case i=1,j=3.

Answer 3

@Kainui @ganeshie8 @welshfella

Answer 4

Heyy

Answer 5

hi!
well brb

Answer 6

bck @ganeshie8

Answer 7

@TheCleverOne I think you might be able to help with this one, you did pretty well helping K12 earlier.

Answer 8

Recall below property of definite integrals :

\[\int_0^a f(x)\,dx = \int_0^af(a-x)\,dx\]

Answer 9

\[I = \int\limits\limits_{0}^{\pi}x\cdot \cos^6x\cdot \sin^5xdx\]

using the previous property of definite integrals, above is same s

\[I = \int\limits\limits_{0}^{\pi} (\pi-x)\cdot \cos^6(\pi-x)\cdot \sin^5(\pi-x)dx \\= \int\limits\limits_{0}^{\pi}(\pi-x)\cdot \cos^6x\cdot \sin^5xdx\]

Answer 10

Add them and get
\[I+I = \int\limits\limits_{0}^{\pi}\pi\cdot \cos^6x\cdot \sin^5xdx \]

Answer 11

Next let \(\cos x = u\) and rest should be easy

Answer 12

oh okay
lag!!!!

Answer 13

wait i got
1/4 \(\frac{\Gama(5/2)\cdot~\Gamma(4)}{\Gamma(13/2)}\)

Answer 14

wolfram says \(\dfrac{8\pi}{693}\)

https://www.wolframalpha.com/input/?i=1%2F2*Integrate [pi\cdot+\cos^6x\cdot+\sin^5x,+{x,0,pi}]