using beta function integration Show that: 1 dx = bu xu-1 В (и, т — и + 1) (1 + bx)m+1 By making the following transformation: bx y = 1 + bx

Q: Differentiate. x4 y: 3 — х3 y' У -

A:

Q: 6. For each of the following series determine if the series converges or diverges using the…

A:

Q: Let R = {(x,y): |x| + |y| ≤ 2}. Use the transformation x=u+v, y=u-v to evaluate ∫∫ ((x^2)*(e^y))dA

A: Consider the given: R=x,y:x+y≤2x=u+vy=u−vA=111−1=−1−1=−2=2

Q: Find the general solution of the DE s

A: Given: - The differential equation is, dydx=2yx+x3y+xtanyx2 To find: - The general solution of the…

Q: Find the Fourier Transforms of the indicated function: f (x) = cos x e−x^2/2

A: The given problem is to find the Fourier transform of the given function. Given function, f(x) =…

Q: Transform the equation: 2x2y'' + xy' + 3y = 0 to the form of: a(d2y/dz2) + b(dy/dz) + cy = 0 (a,…

A:

Q: Let D, be the linear transformation from C'[a, b] into C[a, b). Find the preimage of the function.…

A:

Q: Find div F and curl F if F(x, y, z) = x³i - 10j+yzk. div F= curl F=

A:

Q: F(x, y, z) = yzeX²i + e×zj + xyexZk, C: r(t) = (t2 + 1)i + (t² – 1)j + (t² – 4t)k, %3D 0 <t< 4 (a)…

A: Given,

Q: Find div F and curl F if F(x, y, z)=xi - 10j+yzk. div F= curl F=

A:

Q: Find the general solution u(x,y) of: uxy : 2y. =

A:

Q: Determine whether the following are linear transformations or not. Justify. (1) L(x) = x + 2 where L…

A: The given maps are,(1)  where (2) where The objective is to determine whether the map is a linear…

Q: ·볼+1 2x - y dx dy, Use the transformation to evaluate 2x-y where u = v = % and integrating over an…

A:

Q: Integrate (2x - 5) with respect to x from x = 2 to x = 5.

A:

Q: f(y) { 2ye-y^2 , y > 0         { 0, otherwise Find the G(U) transformation such that if U has a…

A: The probability density function of y f(y)= y&gt;0U~U(0,1) Using FormulaCumulative distribution…

Q: Integrate by substitution: 2e dx 5e2a+1

A:

Q: For which real number a, the solution of the Initial Value Problem is such that x(2) = e. O 1/4 02 O…

A:

Q: Laplace Transformation f(t) = t^3 sint f(t) = ( 1 + cosht) ^ 2 f(t) = sin ^ 2 ( t + π ) f(t) =…

A: Ans:Givenf(t)=t3sintThenLf(t)=?we  know  that Ltng(t)=(-1)ndndSnG(S),where G(S)=Lg(t)----(1)Here…

Q: Use the Fundamental Theorem of Calculus Part I to find dh/dx given h(x) = cost dt (Hìnt: need…

A: Answer:  By fundamental theorem of calculus  Let fx=∫axbx gt. dt   dfdx=gbx.b'x-gax.a'x

Q: Integrate f(x, y) = (x + y + 7)-2 over the triangle with vertices (0, 0), (2, 0), and (0,4). (Use…

A:

Q: CD has coordinates C(-8,-2) and D(-4,-12). determine the coordiantes of C'D' if (x,y) -> (1/2x,1/2y)…

A:

Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: Integrate by change of variable, ∫∫R(x + y)e((x^2)-(y^2))dA, where R is the rectangle enclosed by…

A: We need to evaluate integral.

Q: What are the coordinates of V after the transformation (T • D5)(ATUV) for T(-1,-1), U(-1, 2), V(2,…

A: Given transformation is T3,−2∘D5△TUV for T−1,−1, U−1,2, V2,1. We have to find the coordinates of V…

Q: What is the rule used to transform ΔABC to its image?A(−3, 5), B(2, 8), C(−4, −5) and A'(−3, −5),…

A: The objective of the question is to identify the transformation rule that was used to transform…

Q: Which of the following transformations are linear? А. Т В. Т 8 x + 2 С. Т y, D. T z. 7y Е. Т -4z -9x…

A:

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: Solve the equation (x^2-3y^2)dx + 2xydy = 0 using y=v.x and u transforms

A: