Find the area of the region bounded by the curve of sin x between x = 0
and x = 2π.
Integral of sinx is -cosx . We will find the area up to pi & then double it;So Top limit- Lower limit: -cospi-(-cos0)=+1+1=2. Hence;4
thanks
To find the area of the region bounded by the curve of sin x between x = 0 and x = 2π, you can use the concept of definite integration.
Step 1: Determine the integral expression for the area. Since the curve is defined as sin x, the integral expression for the area is ∫(sin x) dx.
Step 2: Evaluate the definite integral between x = 0 and x = 2π. The integral expression becomes ∫[0 to 2π] (sin x) dx.
Step 3: Calculate the anti-derivative of sin x. The anti-derivative of sin x is -cos x.
Step 4: Apply the Fundamental Theorem of Calculus to evaluate the definite integral. The integral of sin x from 0 to 2π is [-cos x] evaluated from 0 to 2π.
Step 5: Plug in the upper bound (2π) into the anti-derivative expression: -cos(2π).
Step 6: Plug in the lower bound (0) into the anti-derivative expression: -cos(0).
Step 7: Evaluate the expression: -cos(2π) - (-cos(0)). Simplified, this becomes -1 - (-1), which is equal to 0.
Therefore, the area of the region bounded by the curve of sin x between x = 0 and x = 2π is 0 square units.