Find the area bounded by the x-axis, the curve 𝑦 = 𝑐 sin 𝑥/𝑐 and the ordinates x = 0 and x = a, 2𝑎 ≤𝑐π.

Question

Find the area bounded by the x-axis, the curve 𝑦 = 𝑐 sin 𝑥/𝑐 and the ordinates x = 0 and x = a, 2𝑎 ≤𝑐π.

Answer 1

how about you try one or more of these, rather than just leaving a homework dump. They're all pretty straightforward. Show us what you think it involves.

Answer 2

To find the area bounded by the x-axis, the curve 𝑦 = 𝑐 sin 𝑥/𝑐, and the ordinates x = 0 and x = a, you can use the definite integral. The definite integral will allow you to find the area under the curve between the two given ordinates.

Let's break down the steps to find the area:

1. Start by setting up the integral notation for the area:
∫[a, 0] (𝑐 sin(𝑥/𝑐)) dx

2. Simplify the integral by factoring out the constant 𝑐:
(𝑐/𝑐) ∫[a, 0] (sin(𝑥/𝑐)) dx

3. Integrate the function within the given bounds:
-𝑐/𝑐 [cos(𝑥/𝑐)] [a, 0]

4. Substitute the limits of integration:
-𝑐/𝑐 (cos(0/𝑐) - cos(a/𝑐))

5. Simplify the expression further:
- (cos(0) - cos(a/𝑐))

6. Since cos(0) = 1, the expression simplifies to:
- (1 - cos(a/𝑐))

So, the area bounded by the x-axis, the curve 𝑦 = 𝑐 sin 𝑥/𝑐, and the ordinates x = 0 and x = a is - (1 - cos(a/𝑐)).

Please note that the condition 2𝑎 ≤ 𝑐π needs to be incorporated into the limits of integration when evaluating the definite integral.

Find the area bounded by the x-axis, the curve 𝑦 = 𝑐 sin 𝑥/𝑐 and the ordinates x = 0 and x = a, 2𝑎 ≤𝑐π.

how about you try one or more of these, rather than just leaving a homework dump. They're all pretty straightforward. Show us what you think it involves.

hlo

To find the area bounded by the x-axis, the curve 𝑦 = 𝑐 sin 𝑥/𝑐, and the ordinates x = 0 and x = a, you can use the definite integral. The definite integral will allow you to find the area under the curve between the two given ordinates.