Sketch the graph of the curve y = (x – p)(x – p – 1)(x – p – 2) Shade the area of the region bounded by the curve, у %3 (х — р) (х—р — 1)(х — р — 2), the X — ахis, х %3D0 and x %3D р +3 Hence, find the area of the region using integration.

Q: Q1: Evaluate: 2x dV where E is the region under the plane 2x + 3y + z = 6 that lies in the first…

A:

Q: (d) |// Vx² + y² dV, where P is the region under the cone z = 2 – ry-plane. /x² + y² and above the…

A: Since you have asked for a multiple question, we will solve the first question for you. If you want…

Q: Evaluate p (x² – 2xy)dx + (x²y +3)dy around the boundary of the region defined by y? = 8x and x = 2…

A: To evaluate : ∮x2-2xy dx+x2y+3 dy around the boundary of the region defined by y2=8x and x=2 (a)…

Q: Find the area of the surface generated by e + e -y revolving the curve x = 2 0sys In 6 about the…

A: To find the surface area generated by revolving the curve x=ey+e-y2,0≤y≤ln6 about the x-axis. We…

Q: Calculate the integral f, (3y – 3x²) dæ + (9x) dy where y= aD is the counter-clockwise boundary of…

A: we are allow to solve one question at a time thank you

Q: Evaluate the triple integral ∫∫∫T (x^2) dV where T is the tetrahedron with vertices (0, 0, 0), (1,…

A:

Q: Sketch the region of integration and change the order of integration. T/2 cos x f(x, y) dy dx

A:

Q: f(x) = x³, with 0 < x < 1

A: We know, the surface area of the solid that is obtained by rotating the graph of y=f(x) about the…

Q: y2 %3D 1. 60. x²y dx dy dz, T: Region bounded by 4

A:

Q: -x), with respect to OY. 4. The area bounded by the curve 2x+2x -y -2 0 and the line y=2x with…

A:

Q: . 3. Compute E y 2 z 2 dV , where E is the region bounded by x  1
y 2
z 2 and x 

A: The given curves are

Q: 16 The area under the curve 4y? (x2 + 1)3 was rotated about a line located to the left 9 of y – axis…

A:

Q: 5xy dv, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded by…

A: The given integral is ∭E5xydV. The region E lies under the plane z=1+x+y and above the region in the…

Q: Evaluate the triple integral. 16.  ∫∫∫T  xz dV , where T is the solid tetrahedron with vertices…

A: The solid tetrahedron T with vertices 0, 0, 0, (1, 0, 1), (0, 1 ,1) and 0,0, 1. The solid region is…

Q: Hw.3 3 Find the areas for the following Vegions: Region boundded by y=x y , and Region bounded by…

A: To find the area of the following region :-

Q: Q sketch the region of in tegration and evaluate the a) 3 yxy e'dxdy

A:

Q: Find the area of the surface formed by revolving the graph of f(x) = x3 on the interval [0, 1] about…

A:

Q: Calculate the double integral (x + y)²ex* - y² dx dy where R is the square with vertices (2, 0), (0,…

A: According to the given information, it is required to find the integral over R where R is square.

Q: Q3/ Evaluate: 1- SS (4x + 2) for the region enclosed by the curves y = x² and y = 2x 2- Show that…

A: 1. Consider a function of two variables, z=fx,y. The double integral of function fx,y is denoted by…

Q: The surface area of the surface generated by revolving y=1-x² for 0<x<1 about the x- axis is s=…

A: If you like the solution then please give it a thumbs up.... The Answer is:              S =…

Q: Evaluate the triple integral // x dV, where T is the solid tetrahedron with vertices T (0,0, 0),…

A: Here we have to evaluate the triple integral , where T is the solid tetrahedron with vertices…

Q: 4. Use Integration to find the exact area of the region common to r = 3 and r 6 cos(0).

A:

Q: 1. Sketch the region corresponding to the double integral rx+2 dy dx x2 and reverse the order of…

A: One of the two main parts of calculus which are concerned with the study of integrals, as opposed to…

Q: Given (1 + y³)y' = x². (i) Determine a region of the xy-plane for which the given differentia…

A: Explanation of the solution is given below...

Q: Find the value(s) of c such that the area of the region bounded by the parabolae y=x^2 - c^2 and…

A: Given: The given parabolas are y=x2-c2 and y=c2-x2. Determine the points of intersection.…

Q: (1) Sketch the regions of integration. (a) 3m/2 (b) (r,0)r drdo 3m/4

A: The integrations  (a). ∫-π2π2∫04f(r,θ)rdrdθ(b). ∫3π43π2∫34f(r,θ)rdrdθ We have to sketch the regions…

Q: Consider the following line integral. xy dx + x²y dy, Cis counterclockwise around the triangle with…

A:

Q: The solid S is obtained by rotating the region enclosed by y = f(x) 2 0, a = 5+ 5e6 1- e6 5+ 5e16 1-…

A: The given question is solved below.

Q: Given S J. 2. dy dx Rev erve the or der and ev aluate . Show Of Integration the region.

A:

Q: Evaluate the triple integral II. x* dV, where T' is the solid tetrahedron h vertices (0, 0, 0),…

A:

Q: Given the area bounded by the parabola x² – 4x + 12y- 20 = 0, the x- axis and the lines x = 1 and x…

A: Sol

Q: integrate ƒ over the given region. ƒ(s, t) = e^s ln t over the region in the first quad-rant of the…

A:

Q: Find the value of the closed loop integral z3 + sin z -dz (z – i)3 taken around the boundary of the…

A: GIven  ∮z3+sinz(z-i)3dz   To compute this integral we have to use the following theorem. Theorem:…

Q: x² and t %3D 2) = z where E is the region bounded by the parabolic cylinder y

A: We have to set up the integral according to the given information

Q: c) Evaluate Ssin 3.xcos 4x dx by using integration by part.

A: Here we have to find            ∫ sin 3x cos 4x dx Integration by parts formula is          ∫ uvdx =…

Q: $(2xy - x²) dx + (x+y²)dy, where C is the enclosed curve of the region boundec. The value of by y=x²…

A:

Q: You are rotating the region bounded by y 2 = x, y = 1, and x = 0 about the line x = 1. Set up the…

A: First, we sketch the region using a graphing calculator  y2=x , y=1 , x=0 The shaded region is…

Q: I// sin(x²+y²) dV , where E is the region E = {(x, y, z) : x²+y² < 1, 0 <z< 1}. E

A:

Q: The electric potential at each point (x,y) in the region R: x 2 0, y s1 is given by v - 48xy – 32x -…

A:

Q: Consider the integral x³+1 x³(x²+1) -dx What is the correct partial fractio OA Bx + C

A: We have to choose the correct option from the given options according to the given information

Q: (1) Sketch the regions of integration. (a) 7/2 Jo r3m/2 (b) (1r, 0)r drdo 3n/4

A: Consider the equation

Q: Let I = L S x+1 хdydx. %3D -1J-V1-x By reversing the order of integration of I, we obtain: Two…

A:

Q: f(x) = V4x +1, = V4x + 1, with 1< x < 5

A:

Q: A 3 cm length silver bar with a constant cross section area 1 cm" (density 10 g/cm, thermal…

A:

Q: Calculate the double integral || (x + y)?e* - Ý dx dy where R is the square with vertices (2, 0),…

A: According to the given information, it is required to find the integral over R where R is square.

Q: The volume of the solid generated by the curve y = e¯ª, between x = 2 and x = 7 about the x – axis…

A: Given curve, y=e-x x=2  and   x=7

Q: The volume of the solid generated by the curve y = e¬ª, between x = 3 and x = 7 about the |3| x –…

A:

Q: If we rotate the region under the curve y = 8 between x = 2 and x = 3 about the x-axis, what answer…

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.