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The area bounded by the curves y=cosx an...

The area bounded by the curves `y=cosx` and `y=sinx` between the ordinates `x=0` and `x=(3pi)/2` is

A

`4sqrt(2)+1`

B

`4sqrt(2)-1`

C

`4sqrt(2)+2`

D

`4sqrt(2)-2`

Text Solution

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The correct Answer is:
To find the area bounded by the curves \( y = \cos x \) and \( y = \sin x \) between the ordinates \( x = 0 \) and \( x = \frac{3\pi}{2} \), we will follow these steps: ### Step 1: Find the points of intersection We need to find where \( \cos x = \sin x \). This occurs when: \[ \tan x = 1 \] The solutions for this equation in the interval \( [0, \frac{3\pi}{2}] \) are: \[ x = \frac{\pi}{4} \quad \text{and} \quad x = \frac{5\pi}{4} \]
To find the area bounded by the curves \( y = \cos x \) and \( y = \sin x \) between the ordinates \( x = 0 \) and \( x = \frac{3\pi}{2} \), we will follow these steps: ### Step 1: Find the points of intersection We need to find where \( \cos x = \sin x \). This occurs when: \[ \tan x = 1 \] The solutions for this equation in the interval \( [0, \frac{3\pi}{2}] \) are: ...
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