- #1
chjopl
- 21
- 0
Find area between y=Sin x and y=Cos x on intervals [Pi/4, 15Pi/4].
garytse86 said:how do you that the areas won't cancel out? If one is above and the other below the x-axis?
The formula for finding the area between two curves is ∫(upper limit - lower limit) (f(x) - g(x))dx, where f(x) and g(x) are the two functions and the upper and lower limits are the points of intersection between the two curves.
To find the points of intersection, set the two equations equal to each other and solve for x. Once you have the x-values, plug them back into one of the equations to find the corresponding y-values.
Yes, you can use the formula mentioned in question 1 to find the area of a specific region between the two curves. Just make sure to set the upper and lower limits accordingly.
No, the area between two curves is always a positive value. If you get a negative value, it means you have set the limits incorrectly or calculated the integral incorrectly.
No, finding the area between two curves requires the use of integration. There may be other methods to approximate the area, but integration is the most accurate way to calculate it.