How do you find the area of a region bounded by a line and a curve?

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. This means that you have to be careful when finding an area which is partly above and partly below the x-axis.

What is the total area of regions between the curves y 6x 2 18x and y 6x?

8 sq. units
Hence, the total area of the region bounded by y=6×2−18x y = 6 x 2 − 18 x and y=−6x y = − 6 x is 8 sq. units.

Is the relation Y XA function?

A function is a relation in which each input has only one output. In the relation , y is a function of x, because for each input x (1, 2, 3, or 0), there is only one output y.

How do you find the area of a curve region?

The area of the region between the curves is defined as the integral of the upper curve minus the integral of the lower curve over each region. The regions are determined by the intersection points of the curves. This can be done algebraically or graphically. Integrate to find the area between 0 0 and 4 4.

How do you find the intersection of two curves?

Solve by substitution to find the intersection between the curves. Tap for more steps… Substitute x 2 x 2 for y y into y = 2 x y = 2 x then solve for x x. Tap for more steps… Replace y y with x 2 x 2 in the equation. Solve the equation for x x. Tap for more steps… Subtract 2 x 2 x from both sides of the equation.

How do you find the coordinates of intersection?

To find the coordinates of intersection: So the intersection coordinates are: We can calculate the bounded area (shaded) by integrating either wrt x or wrt y, the latter being easier.

How do you find the area of a thin vertical strip?

Thus, the area is given by: if we integrate with infinestimall thin vertical striops then we find the strips are bounded by 4x +y2 = 32 at the bottom and y = x at the top but only when x is between the lower point of intersection ( − 8, − 8) to the upper point of intersection (4,4)