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Answer: d
Explanation: dM/dx = cos x and dL/dy = -sin y
∫∫(dM/dx – dL/dy)dx dy = ∫∫ (cos x + sin y)dx dy. On integrating with x = 0->90 and y = 0-
>90, we get area of right angled triangle as -180 units (taken in clockwise direction).
Since area cannot be negative, we take 180 units.
To find the area of a right-angled triangle, we need the lengths of the two perpendicular sides. However, based on your request, it seems you are mentioning only a 90-degree unit which might imply the two sides are of equal length, typically representing a right-angled triangle with sides of 1 unit each.
The area ( A ) of a right-angled triangle can be calculated using the formula:
[
A = frac{1}{2} times text{base} times text{height}
]
Assuming both the base and height are 1 unit, the area would be:
[
A = frac{1}{2} times 1 times 1 = frac{1}{2} text{ square units}
]
As for the functions described by ( L = cos y ) and ( M = sin x ), these do not directly affect the area calculation of the triangle unless specified as part of further geometry or context.
Therefore, the area of the right-angled triangle is:
[
text{Area} = frac{1}{2} text{ square units}
]