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Integrate f(x,y)=x2 + y over the triangular region with vertices (0,0), (1,0), and (0,1). The value...
A triangular lamina in the xy-plane such that its vertices are (0,0), (0,1) and (1,0). Suppose that the density function of the lamina is defined by p(x,y) = 15xy gram per cubic centimetre. Use the information given to answer the following questions (2 decimal places): The centre of gravity of the lamina ( 2,7) is ).
Q) Calculate ;) SS the value of the double integral triangular region with vertices (0,0), (1, 1) and (0,1)) 16. 1} dA 5 & 1 + x2 ;;;) SlxdA ; R R x=8- y² I quadrant between the circles' x² + y² = 1 and x² + y²=2 circles}
3. Let S be the triangle with vertices at (0,0), (1,0) and (0,1). Let f (x, y) = e***. Use the change of variables u = x – y, v = x +y to find . f(a,y) dA.
(15 points) The triangular region with vertices (0,0), (1,0) and (0,6) is rotated aboutthe line x= 3. Find the volume of the solid so generated.(Sketch the region and the solid obtained. Write down the name of the method used.)
5 ve 6. Soru Dry - xdA over the triangle with vertices ( -1,0), (0,0) and (0,1) changing the variables by u = y - x and v = y + x. (DONOTEVALUATE INTEGRAL) 1 w 5. (15 points) Write the integral representing the area of the region al < x2 + y2 < band below the line y = x in polar coordinates.(DONOT EVALUATE INTEGRAL) ,y,z) as an iterated integral in cartesian coor- dinates. E is the region inside...
please show all work with steps Integrate f(u,v) =v- Vu over the triangular region cut from the first quadrant of the uv-plane by the line u + v= 16 The integral value is 0 (Type an integer or a simplified fraction.)
Verify Green's theorem for the triangular region with the vertices (0,0), (1,2), and (0,2) and the vector field F(x,y) = 2y2i + (x + 2y)?j.
10) Integrate f(x, y) = sin (Vx2 + y2) over the region 0 < x2 + y2 = 16
4. Evaluate (2 + y)dA, where D is the triangle with vertices (0,0), (0,1),(1,0).
find Ssey R R is a triangular region in x-y plane with vertices (-2, 2), (0,0), (2, 2)