How do you find the area between the function and the x-axis?

The area under a curve between two points can be found by doing a definite integral between the two points. To find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. Areas under the x-axis will come out negative and areas above the x-axis will be positive.

What is the formula for area of a shaded region?

The Area of the shaded region = (Area of the largest circle) – (Area of the circle with radius 3) – (Area of the circle with radius 2). Whatever is left over is the shaded region. The diameter of the largest circle is 10, so its radius is 5 and thus its area is 25π.

What is the area between the graphs of f(x) and g(x)?

We find that g(x) is above f (x) in the area that they share, so we find the area under g(x), and will subtract the area of f (x) from that. Now subtract the two areas. Hence, the area between the graphs of f (x) = x2 + 2x + 1 and g(x) = 3x +3 is 4.5 units2. Hopefully this helps!

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 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 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 .