The area between the curve `y=cosx` and Y-axis from y = 0 to y = 1 is

Options

A. 1
B. 2
C. `sqrt(2)-1`
D. `pi`

Answer

To find the area between the curve \( y = \cos x \) and the Y-axis from \( y = 0 \) to \( y = 1 \), we can follow these steps:

### Step 1: Identify the points of intersection
We need to find the values of \( x \) for which \( y = \cos x \) intersects the lines \( y = 0 \) and \( y = 1 \).

1. For \( y = 1 \):
\[ \cos x = 1 \implies x = 0 \]

2. For \( y = 0 \):
\[ \cos x = 0 \implies x = \frac{\pi}{2} \]

Thus, the points of intersection are \( x = 0 \) and \( x = \frac{\pi}{2} \).

### Step 2: Set up the integral for the area
The area \( A \) between the curve and the Y-axis from \( x = 0 \) to \( x = \frac{\pi}{2} \) can be expressed as:
\[ A = \int_{0}^{\frac{\pi}{2}} \cos x \, dx \]

### Step 3: Evaluate the integral
Now we will evaluate the integral:
\[ A = \int_{0}^{\frac{\pi}{2}} \cos x \, dx \]

The integral of \( \cos x \) is \( \sin x \):
\[ A = \left[ \sin x \right]_{0}^{\frac{\pi}{2}} = \sin\left(\frac{\pi}{2}\right) - \sin(0) \]

Calculating the values:
\[ \sin\left(\frac{\pi}{2}\right) = 1 \quad \text{and} \quad \sin(0) = 0 \]

Thus:
\[ A = 1 - 0 = 1 \]

### Conclusion
The area between the curve \( y = \cos x \) and the Y-axis from \( y = 0 \) to \( y = 1 \) is:
\[ \boxed{1} \text{ square unit} \]

---