y y = x' - 2 x 4 2 -4 -2 2 -2 y = 2 x -6F (a) Find the points of intersection of the curves. (х, у) %3 (smallest x-value) (х, у) = (х, у) (largest y-value) (b) Form the integral that represents the area of the shaded region. 0. ' 2 dy + dy

Q: A tank is filled with a fluid with density 54 The cross-section of the end of the tank is given by…

A: The slice is shown below:The volume of slice is,

Q: if x~unif. (0,2),find the U.b. of p(lx - mul>= 2)

A: Given X~Unif(0,2) Result: if X~unif(a,b) then  Mean=(a+b)/2 Variance=(b-a)2/12

Q: If z = In(x² – 2y), and x=u+v, y= e" , find and du If w=2xy'z', and y =x² +1, z= Vx, find dx

A:

Q: y = x - 2x 4 -2 y = 2 x (a) Find the points of intersection of the curves. (x, y) = (smallest…

A: Given query is to find the intersection point and shaded area for the curves.

Q: Prove that for all n E N, 1 1x 2 x 3 n(n + 3) 4(n + 1){n + 2 1 1 2 x 3 x 4 n(n + 1)(n+2)

A:

Q: y = x^(2) , y = x^(3) find the area by rotating around the y axis

A:

Q: y-1/10(e^(5x)+e^(-5x)), for x:[-4,4], about the x axis. Find surface area

A: Let's find surface area.

Q: Suppose A = {1, 2} and B = {2, 3). Answer the following using numberic values only. a. 9(ANB) c.…

A:

Q: 1 – 2x + 3x² 1 + x² - The normal to y : at (0, 1)

A: Consider the given polynomial  y=1-2x+3x21+x2 First, find the first derivative of the function…

Q: Find the area of the region bounded by the curve y=1--x² and the x-axis. 9 6 square units 4 square…

A:

Q: Can i get help step by step please?

A:

Q: y = v2x + (1//2) х2 +1

A:

Q: To/t Integrate Ua ko To 3. Uz kg 2. eT-1

A:

Q: Find the area under the curve

A: To find area under the curve defined by the points (20,85), (15,83), (9,80) & (7,78)We can use…

Q: Find of / dx and of /ay. f(x.y) = elx +y+6) of I dx = of I dy =

A:

Q: Find equations of the tangent plane and normal line to the surface x = 5y² + 5z² — 28 at the point…

A:

Q: Find the area of the plane region that lies below the line y = 2x and between the parabolas y= 2x^2…

A: Given Curves are:…

Q: y = x - 15 x 10 y = x (4, 4) -6 -4 4 K-4,-4) - 10 - 20 20

A:

Q: Find the points of intersection of the graphs of the functions y = (x − 4)³ and y = 6(x − 4) 4,8,0…

A: Step 1: To find the intersections of the functions, we will equate the two equations and solve for…

Q: (a) Find the area of the surface generated by the given curve about x-axis y = V, (b) Find the area…

A:

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: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)^2=2y , the…

A:

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.