How do you find the area of the region between curves?
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. Combine the integrals into a single integral. Multiply −1 – 1 by x2 x 2.
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 solve x(x – 2) = 0 true?
The final solution is all the values that make x ( x − 2) = 0 x ( x – 2) = 0 true. Substitute 0 0 for x x into y = 2 x y = 2 x then solve for y y. Tap for more steps… Replace x x with 0 0 in the equation. Multiply 2 2 by 0 0. Substitute 2 2 for x x into y = 2 x y = 2 x then solve for y y. Tap for more steps…
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. Area = ∫ 1 0 xdx−∫ 1 0 x2dx A r e a = ∫ 0 1 x d x – ∫ 0 1 x 2 d x
How do you find the area between f y and g y?
To find the area between f ( y) and g ( y) over the interval [ c, d], take the integral of the function to the right minus the function to the left. Think about it: the area between the two curves is equal to the area under the top function minus the area that is under the bottom function.
Solve by substitution to find the intersection between the curves. Tap for more steps… Substitute x 2 x 2 for y y into y = 4 x − x 2 y = 4 x – x 2 then solve for x x. Tap for more steps… Replace y y with x 2 x 2 in the equation.
How to find the area between 0 and 1?
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 1 1. Tap for more steps… Combine the integrals into a single integral.