Online Area Between Two Curves Calculator helps you to evaluate the equations and give the exact area between two curves in a short span of time. Simply provide the two equations in the input field of the tool and click on the calculate button to check the accurate output in just seconds.
Area Between Two Curves Calculator: Students who are looking for the easiest way to find the area between two curves can make use of this handy calculator tool. Apart from the tool, you will also get the learning stuff like step by step process to find the area between two curves in detail with solved example. So, check the below sections, to get a good knowledge on the area between two curves topic and get your answers effortlessly.
Steps to find Area Between Two Curves
Follow the simple guidelines to find the area between two curves and they are along the lines
- If we have two curves P: y = f(x), Q: y = g(x)
- Get the intersection points of the curve by substituting one equation values in another one and make that equation has only one variable.
- Solve that equation and find the points of intersection.
- Draw a graph for the given curves and point of intersection.
- Then area will be A = ∫x2x1 [f(x)-g(x)]dx
- Substitute the values in the above formula.
- Solve the integration and replace the values to get the result.
Example
Question: Calculate the area of the region bounded by the curves y2 + 4x – y = 0 and the straight line y = x?
Solution:
Given equations are y2 + 4x – y = 0, y=x
y2 + 4x – y = 0
Add y and subtract y2 on both sides.
y2 + 4x – y + y – y2 = y – y2
4x = y – y2
Divide by 4 on both sides
x = y – y2/4
Using another equation y = x in the equation of the curve will be
y2+4y-y = 0
y2+3y = 0
y(y+3) = 0
y = 0 or -3
Corresponding to the values of y, we get x = 0 or -3. Thus the points of intersection are P(-3,-3) and Q(0,0).
The graph for the system will be:
From the graph, the curve on the right is f(y) and the curve on the left is g(y).
f(y) = y – y2/4
g(y) = y
The area is A = ∫x2x1 [f(x)-g(x)]dx
A = ∫30 [(y – y2/4)-y]dy
= ∫30 ((-y2-3y)/4)dy
= [ – y3/4*3 – 3/4 * y2/2]30
= – [(0+0) – (- 33/4*3 – 3/4 * 32/2)
= – ( -27/12 + 3/4 * 9/2)
= 27/24
Area as specified by the definite integral is -27/24.
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FAQs on Area Between Two Curves Calculator
1. What is the area between two curves?
The area between two curves is calculated by computing the difference between the definite integrals between two functions. In a two dimensional geometry, the area is a quantity that expresses the region occupied by the equations.
2. What is meant by the polar curve?
A polar curve represents a shape whose construction takes place by using the polar coordinate system. They are marked by points that exist a variable distance from the origin or pole.
3. What is the area under the curve?
The area under a curve is present between two points and can be calculated by conducting a definite integral between those two points. To find the area under the curve y = f(x) between x = a and x=b, you must integrate y = f(x) between the limits of a &b.
4. Find out the area of the region enclosed by y = sin x, y = cos x, x = π/2, and the y-axis?
From the given equations
sin x = cos x
At this interval, x = π/4.
The area will be,
A = ∫0π/4 cos x – sin x dx + ∫π/4π/2 sin x – cos x dx
= [sin x + cos x]0π/4 + [-cos x – sin x]π/4π/2
= (sin (π/4) + cos (π/4)) – (sin 0 + cos 0) + (-cos (π/2) – sin (π/2)) – (-cos (π/4) – sin (π/4))
= (√2/2 + √2/2) – (0+1) – (0+1) + (√2/2 + √2/2)
=2√2-2 = 0.828427.
5. Is it possible for the area between two curves to be negative?
No, the area between two curves will never be negative. Because, the area between two curves is not like the area under the curve. Hence, the area between the two curves is always positive.