1. Draw a triangle with vertices A(0, 1), B(2, 0), C(3, 4) and use integration to find its area.

Q: Evaluate O xy?dx + a°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3)

A:

Q: Find the value of c > 0 such that the regionbounded by the cubic y = x(x - c)2 and the x-axis on…

A:

Q: The sides of a triangle are 26, 28, and 34 cm. Centered at each vertex are three circles, tangent…

A:

Q: Calculate the length of the astroid of x + y² = 2 2 X 3 1. S= ←

A:

Q: Calculate the double integral Sle (x² + 2y) dA, where R is the triangular region with vertices 8/3…

A:

Q: .Find the exact value of the double integral. J (2x + 5y) dA, where R is the rectangular region…

A:

Q: 5.2 Compute I = e -dz, where C is the boundary of the square centred at the origin, with sides of…

A:

Q: If R is the region boundeb by the square a|+|y = 1 then ffR(y-2)dA is equal

A:

Q: The numerical value of 34 3dA (where D is the region bounded by lines y=0 and x = 1, D and the…

A:

Q: Fined Fhe boundled by Ahe Cure area 2. x+Y= 3 %3D -33-j` and ど= %3D Ans wer

A:

Q: The area bounded by the curve y3a and the lines z 4 and a-9 above the z-azis is aquare units O 27v0…

A:

Q: 17. Find the exact area of the surface z = 1 + 2x + 3y + 4y2, 1x 4, 0 y < 1

A:

Q: Verify Green's Theorem by evaluating both integrals | y2 dx + x2 dy dA ду for the given path. C:…

A:

Q: If b = 6 cm, c = 3 cm, h = 6 cm, and a = 2 cm, the centroid of the area about x axis is equal to:…

A:

Q: y=x², y = 1, y =9 y=9, first quadrant

A:

Q: If C is the line segment from (1, 3) to, (0, 0), find the value of the line integral: 3y i+ 3x j) ·…

A: Given If C is the line segment from (1, 3) to, (0, 0),

Q: In Exercises 17-20, find the area of the shaded region in Figures 16-19.

A: Consider the following diagram:

Q: If C is the line segment from (1, 3) to, (0, 0), find the value of the line integral: So(3y² i +3xj)…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 8- Solve ihe separation of variable MeRod satisfy %3D The condilion as tp0 as for x=0 and a =a T=メ…

A:

Q: Solve u +u =0 for the square mesh with boundary values as shown in Figure 11.14. Iterate till the…

A: Consider the given differential equation, uxx+uyy=0 Here we have to find the mess values which are…

Q: 10.18. Use an appropriate change of variables to evaluate the integral ff,(1 + x? + y²)²dA, where T…

A:

Q: If C is the line segment from (1,3) to, (0, 0), find the value of the line integral: S(3y² i +3x}) ·…

A:

Q: (b) ſf f(x,y) dA if f(x, y) = y², where R is the triangular region with vertices (0, 1), (1, 2) and…

A:

Q: Integrate Xy ed २ over the triangular region with vertices: (0,0), ), (0,8) (0,16)

A:

Q: 1.13 Evaluate the line integral $ x*dx + xydx where C is the triangle with vertices at (0, 0), (0,…

A: The given function is x4dx+xydy By green's theorem, the integral becomes, ∫06∫06∂M∂y-∂N∂xdxdy where…

Q: 4. A 5m x 5cm is cut from a corner of 20cm x 30cm. cardboard, find the centroid from the longest…

A:

Q: Among all rectangular regions 0&lt;=x &lt;=a, 0&lt;=y&lt;=b, find the one for which the total…

A:

Q: The shape of a redwood tree (without any branches) can be modeled by an upside down paraboloid, f(x,…

A:

Q: f(x, y) = xy over the triangular region with vertices (0, 0), (8, 0), and (0, 6) O 12 2 96 O 16

A: Solve

Q: Surface Area top front width length area of front = h x w area of top = w x 1 area of bottom = w x 1…

A: Explanation of the answer is as follows

Q: What is the area of a sector ACB? Leave your answer in terms of T. A 10g 5ft

A: Given Radius, r = 5ft.  And angle theta = 108 degree

Q: 2.7 Describe cll soilutions of Asso where A is the Yow ta the matirix meg Vse Y S, and/or t as in…

A: Given  A=1-6-50-2-100100-200001-7000000 Here, we have to solve Ax=0

Q: 10 The double integral 2x dædy, where T is the triangle with vertices (0,0), (3,0) and (6,3), equals

A:

Q: Evaluate the double integral. 8y2 dA, D is the triangular region with vertices (0, 1), (1, 2), (4,…

A: we have to find given double integral

Q: Given: ARST = AXYZ; SK bisects ZRST; K YL bisects 2XYZ. Prove: SK = YL S

A: Prove SK≅YL.

Q: Q1- Determine the coordinates of the centroid of the area.: (1, 1) y= x,

A: The given problem is to find the centroid of the given shaded area of the region formed by given…

Q: 6. Find the area and centroidal distances of the curve that lies between the equations y-4-x^2 and…

A:

Q: Findd Fhie boundled by Ahe Cureo area 2. X= 3J-y' and x+Y=3 ーレ

A:

Q: #1. Evaluate (2x – 5y) dA, R where R is the parallelogram with vertices (0,0), (2,3), (–1,4) and…

A: The given region R is a parallelogram with vertices as shown in below graph. We have to use change…

Q: In his work Nova stereometria doliorum vinariorum (New Solid Geometry of a Wine Barrel), published…

A:

Q: If C is the line segment from (8, 1) to, (0,0), find the value of the line integral: Se(8y² i+x3) ·…

A: First we have to write the equation of the line segment C and then convert the given line integral…

Q: Calculate the double integral ∬R(x2+y2)dxdy in the circle x2+y2=2x.

A: Write the equation of circle into standard form. The radius of the circle is 1.

Q: Question 1 The value of the line integral (x²ydx + 2y2dy), where n is the square with vertices…

A: Note :-  as per our guidelines we are supposed to answer only one question. Kindly repost other…

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: Q1- Determine the coordinates of the centroid of the area.: (1, 1)

A: We need to find the x coordinate and y coordinate of the shaded region which is bounded by two…

Q: Evaluate the double integral. 6y? dA, D is the triangular region with vertices (0, 1), (1, 2), (4,…

A:

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (5,0,0), (0,6,0), and (0,0,3)

A: This question is related to triple integral, We will solve it using given information.

Q: Find the areas of the regions Inside the six-leaved rose r2 = 2 sin 3θ

A: