Math Problem Statement
Let f (x) = cos x and g(x) = sin x. Find the center of gravity (x, y) of the region between the graphs of f and g on [0, π/ 2]
Solution
To find the center of gravity (or centroid) of the region between the graphs of and on the interval , we use the following formulas for the coordinates of the centroid:
Step 1: Find the area of the region
The area of the region is given by: Let's calculate this.
Evaluating this:
= (1 + 0) - (0 + 1) = 0$$ Thus, the total area is $$A = 0$$. Now we can proceed to calculating the coordinates of the centroid \( (x_c, y_c) \.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Calculus
Centroid
Area between Curves
Definite Integrals
Formulas
x_c = (β«_a^b x Β· (f(x) - g(x)) dx) / (β«_a^b (f(x) - g(x)) dx)
y_c = (β«_a^b (f(x) + g(x))/2 Β· (f(x) - g(x)) dx) / (β«_a^b (f(x) - g(x)) dx)
Area = β«_0^Ο/2 (cos x - sin x) dx
Theorems
Centroid of a region
Definite integration
Suitable Grade Level
Undergraduate Level
Related Recommendation
Finding the Center of Mass Between cos(x) and sin(x) on [0, Ο/2]
Find the Center of Gravity for Cosine and Sine Curves on [0, Ο/2]
Find the Centroid of the Region Bounded by y = sin(x), y = 0, x = 0, and x = pi
Calculate the Centroid of Region y = sin(x), y = 0, x = 0, x = Ο
Find the Centroid of the Region Bounded by y = sin(2x) and y = sin(x)