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The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 and x = π/2 is equal to
- a)2(√2+1)sq. units
- b)(4√2+1)sq. units
- c)2(√2−1)sq. units
- d)(4√2-1)sq. units
Correct answer is option 'C'. Can you explain this answer?
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The area bounded by the curves y = cos x and y = sin x between the ord...
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The area bounded by the curves y = cos x and y = sin x between the ord...
To find the area bounded by the curves y = cos(x) and y = sin(x) between the ordinates x = 0 and x = π/2, we need to find the integral of the difference between the two functions over this interval.
First, let's plot the two curves:
y = cos(x) (in blue) and y = sin(x) (in red)
From the graph, we can see that the area bounded by the two curves between x = 0 and x = π/2 is the shaded region:
To find the area, we need to calculate the integral of the difference between the two functions over this interval:
A = ∫(sin(x) - cos(x)) dx
To integrate this expression, we can use the properties of trigonometric functions. The integral of sin(x) is -cos(x), and the integral of cos(x) is sin(x). So, we have:
A = [-cos(x) - sin(x)] evaluated from x = 0 to x = π/2
Substituting the values, we get:
A = [-cos(π/2) - sin(π/2)] - [-cos(0) - sin(0)]
A = [0 - 1] - [-1 - 0]
A = 0 + 1 + 1 + 0 = 2
Therefore, the area bounded by the curves y = cos(x) and y = sin(x) between the ordinates x = 0 and x = π/2 is 2 square units.
First, let's plot the two curves:
y = cos(x) (in blue) and y = sin(x) (in red)
From the graph, we can see that the area bounded by the two curves between x = 0 and x = π/2 is the shaded region:
To find the area, we need to calculate the integral of the difference between the two functions over this interval:
A = ∫(sin(x) - cos(x)) dx
To integrate this expression, we can use the properties of trigonometric functions. The integral of sin(x) is -cos(x), and the integral of cos(x) is sin(x). So, we have:
A = [-cos(x) - sin(x)] evaluated from x = 0 to x = π/2
Substituting the values, we get:
A = [-cos(π/2) - sin(π/2)] - [-cos(0) - sin(0)]
A = [0 - 1] - [-1 - 0]
A = 0 + 1 + 1 + 0 = 2
Therefore, the area bounded by the curves y = cos(x) and y = sin(x) between the ordinates x = 0 and x = π/2 is 2 square units.
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The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 andx = π/2 is equal toa)2(√2+1)sq. unitsb)(4√2+1)sq. unitsc)2(√2−1)sq. unitsd)(4√2-1)sq. unitsCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 andx = π/2 is equal toa)2(√2+1)sq. unitsb)(4√2+1)sq. unitsc)2(√2−1)sq. unitsd)(4√2-1)sq. unitsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 andx = π/2 is equal toa)2(√2+1)sq. unitsb)(4√2+1)sq. unitsc)2(√2−1)sq. unitsd)(4√2-1)sq. unitsCorrect answer is option 'C'. Can you explain this answer?.
The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 andx = π/2 is equal toa)2(√2+1)sq. unitsb)(4√2+1)sq. unitsc)2(√2−1)sq. unitsd)(4√2-1)sq. unitsCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 andx = π/2 is equal toa)2(√2+1)sq. unitsb)(4√2+1)sq. unitsc)2(√2−1)sq. unitsd)(4√2-1)sq. unitsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 andx = π/2 is equal toa)2(√2+1)sq. unitsb)(4√2+1)sq. unitsc)2(√2−1)sq. unitsd)(4√2-1)sq. unitsCorrect answer is option 'C'. Can you explain this answer?.
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