Question

Find the area of the region between the curve y=cost

and the horizontal axis for 0<=t<=π/3 Round answer to three decimal places.

Answer 1

To find the area between the curve y=cos(t) and the horizontal axis for 0<=t<=π/3, use the formula for finding the area under a curve and evaluate the integral.

Step-by-step explanation:

To find the area of the region between the curve y=cos(t) and the horizontal axis for 0<=t<=π/3, we can use the formula for finding the area under a curve. In this case, the area is equal to the integral of the curve from 0 to π/3. The integral of cos(t) is sin(t), so the integral becomes:

A = ∫[0,π/3] cos(t) dt = sin(t) ∣[0,π/3] = sin(π/3) - sin(0)

Using the values sin(π/3) and sin(0), we can calculate the area between the curve and the x-axis for the given range of t.