How do you find the area bounded by a parabola and a line?

Thus, the area between the x – axis and the parabola is \[\dfrac{8\sqrt{2}{{a}^{2}}}{3}\]. Therefore, the area between the straight line and parabola is given as the difference between the area under the line and the area under the parabola.

What is the area of the region bounded by the curve y x2 and the line y 4 is?

∴ Area of the region is given by 32/3 units.

What is area bounded?

a the extent of a two-dimensional surface enclosed within a specified boundary or geometric figure.

What does the area between two curves represent?

Then, the area between two graphs will tell you the difference in displacement between the initial positions and final positions of the particles.

What is the formula to find the area of a parabola?

So, the formula indicates that to find the area under a parabola when it is cut by a horizontal line, we simply multiply two-thirds by the product of the length of the line segment between the points of intersection and the distance from the horizontal line to the vertex.

What is the area bounded by the curve y^2=x and the line x–4=0?

Solution: What is the area bounded by the curve y^2=x and the line x–4=0? What is the area (in square units) bounded by the curve y^2 = x and the line x – 4 = 0? An error occurred. Please try again later The area of the region bounded by the line and curve is 32/3 sq. units.

How do you find the area between X and Y?

In the first case we want to determine the area between y = f (x) y = f ( x) and y =g(x) y = g ( x) on the interval [a,b] [ a, b]. We are also going to assume that f (x) ≥ g(x) f ( x) ≥ g ( x). Take a look at the following sketch to get an idea of what we’re initially going to look at.

How do you find the area between two curves?

In this section we are going to look at finding the area between two curves. There are actually two cases that we are going to be looking at. In the first case we want to determine the area between y = f (x) y = f ( x) and y =g(x) y = g ( x) on the interval [a,b] [ a, b].

How do you find the area of a region with two lines?

Instead we rely on two vertical lines to bound the left and right sides of the region as we noted above Here is the integral that will give the area. Example 3 Determine the area of the region bounded by y = 2×2+10 y = 2 x 2 + 10 and y =4x+16 y = 4 x + 16 .