Question

Find the exact area under the cosine curve y = cos x from x = 0 to x = b, where 0 ≤ b ≤ π/2. (Use a computer algebra system both to evaluate the sum and compute the limit.) In particular, what is the area if b = π/2?

Answer 1

To find the exact area under the cosine curve y = cos x from x = 0 to x = b, where 0 ≤ b ≤ π/2, we can evaluate the definite integral of cos x from 0 to b. The area is equal to sin(b). If b = π/2, the area is 1.

Step-by-step explanation:

To find the exact area under the cosine curve y = cos x from x = 0 to x = b, where 0 ≤ b ≤ π/2, we can evaluate the definite integral of cos x from 0 to b. Since the integral of cos x is sin x, the area under the curve is equal to sin(b) - sin(0) = sin(b) - 0 = sin(b).

To find the area if b = π/2, we substitute b = π/2 into the formula for the area: sin(π/2) = 1.