Find . F.dr when F(x,y) = (2x,3y²) and C is only the first quadrant part of a circle of radius 3 centered at the origin oriented clockwise.

Q: Evaluate ∫ C ( 2 + x^2 y ) d s , where C is the upper half of the unit circle.

A: We have to evaluate the line integral: ∫C2+x2yds where C is the upper half of the unit circle.

Q: Find the distance between two points (1, 2) and (3, −1).

A: We want to find the distance between the given two points. We use formula for finding the distance…

Q: Are the points H and L collinear? U S E H.

A: Collinear means the points which lie on the same line.  From the image, we see that H and L lie on a…

Q: Find the distance between the plances 3x +y-4z = 2 and 3x+ y- 4z = 24

A: Find the distance between the planes   3x+y-4z=2    and    3x+y-4z=24

Q: Find the distance d between the points (1, 3) and (5, 6).

A: Our Aim is to find the distance between the points (1,3) and (5,6).

Q: Draw a diagram showing two perpendicular lines that intersecton the -axis and are both tangent to…

A: The given parabola equation , y=x2. To draw two perpendicular lines that intersect on the axis and…

Q: Sketch the curve y cu. = x sq.

A: Given the curve is y3 = x2 Put random value in the curve and we get the table which help to trace…

Q: Find the area of the circle whose center is at (2, -5) and tangent to the line 4x+3y-8=D0

A: Area of the circle = 9π sq.units

Q: Q6. Evaluate (2yx² - 4x)ds, where C is the lower half of the circle centered at the origin of radius…

A: check belowExplanation:Step 1:Step 2:Step 3: Step 4:

Q: A В 50° 80 ft

A: We can see that it is a right angle triangleGiven BC =80ft∠B =50°we need to find AB

Q: -2 8 and y = 4 Find the distance between x = - 8 The distance between x and y is (Type an exact…

A:

Q: Find the angle between y=5x2-3 and 3xy-9x2-x

A: Given y=5x2-3 --- Eq 1 and 3xy=9x2-x      --- Eq 2We know that angle between y1=k1x+b1 and y2=k2x+b2…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.