4) Let R be the region in the upper half of the xy-plane bounded by x² + y? = 4, y = V3x, x = -y (see the figure). E valuate the integral /- dA. x² + y² x² + y² = 4 x = -y y = /3x

Q: Find the area of part of sphere x² + y? + z² = 100 that lies inside x2 + y? = 10x %3D %3D

A: This is a problem of surface integral.

Q: Find the of the region bounded by the parabolas y – 6x = -x² and y + 2x = x² , area

A:

Q: Compute area of the region bounded byx2+ (y−1)2= 9 andy=x+ 1 and the (horizontal) liney= 1 (we…

A:

Q: Q2: f(x. y)- x/y over the region in the first quad- rant bounded by the lines y x,y 2x,x 1,x-2

A:

Q: y=x² (-2,4) 0 (1,6) (2,4) 3y = 2x + 16 y=-2x+8 X

A:

Q: Find the area bounded by the region y = 2x + 2 and the lines y = 1, y = 2

A:

Q: Q1) Find plane area bounded by y = 2,y = 6 – x, and y = 8 - 3x using double %3D

A:

Q: A region in the xy-plane is bounded by y = 2x + 2, X = y + 2, y = -2, 2 y = 2. and

A: Given curves are y=2x+2 and x=y22+2 The limits are y=-2 and y=2 We isolate x from the first curve,…

Q: 2.- Let R be the region of the xy plane bounded by the graphs y = x^2; y = 2x, evaluate: L(x³ +4y)…

A:

Q: Q3/ Find the area of the following surface z = x² + y lies in region x2 +y = 4.

A: Surface area is defined as a combined sum of all areas or parts and faces of the surface on a three…

Q: 2. Find the area of the region bounded by y = 2x² +10, y = 4x+16, x = -2, and x = 5.

A: first draw bounded region then find limit of region and using vertical strips find the area

Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx