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If ∫(sin 2x - cos 2x)dx = (1/√2) sin (2x-a) + b
- a)a=(π/4), b=0
- b)a=-(π/4), b=0
- c)a=(5π/4), b=constant
- d)a=-(5π/4), b=constant
Correct answer is option 'D'. Can you explain this answer?
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If ∫(sin 2x - cos 2x)dx = (1/√2) sin (2x-a) + ba)a=(π/4),...
Explanation:
Given Integral:
∫(sin 2x - cos 2x)dx
Integration of sin 2x:
The integral of sin 2x with respect to x is -1/2 cos 2x + C1, where C1 is the constant of integration.
Integration of cos 2x:
The integral of cos 2x with respect to x is 1/2 sin 2x + C2, where C2 is the constant of integration.
Substitute the integrals back:
Therefore, the given integral becomes -1/2 cos 2x + 1/2 sin 2x + C, where C is the constant of integration.
Expand the trigonometric functions:
-1/2 cos 2x + 1/2 sin 2x can be rewritten as (1/√2) sin(2x + (3π/4)).
Comparison with the given expression:
To match the given expression (1/√2) sin(2x - a) + b, we need to have a = -(5π/4) and b = constant.
Therefore, the correct answer is option 'D', where a = -(5π/4) and b = constant.
Given Integral:
∫(sin 2x - cos 2x)dx
Integration of sin 2x:
The integral of sin 2x with respect to x is -1/2 cos 2x + C1, where C1 is the constant of integration.
Integration of cos 2x:
The integral of cos 2x with respect to x is 1/2 sin 2x + C2, where C2 is the constant of integration.
Substitute the integrals back:
Therefore, the given integral becomes -1/2 cos 2x + 1/2 sin 2x + C, where C is the constant of integration.
Expand the trigonometric functions:
-1/2 cos 2x + 1/2 sin 2x can be rewritten as (1/√2) sin(2x + (3π/4)).
Comparison with the given expression:
To match the given expression (1/√2) sin(2x - a) + b, we need to have a = -(5π/4) and b = constant.
Therefore, the correct answer is option 'D', where a = -(5π/4) and b = constant.
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If ∫(sin 2x - cos 2x)dx = (1/√2) sin (2x-a) + ba)a=(π/4), b=0b)a=-(π/4), b=0c)a=(5π/4), b=constantd)a=-(5π/4), b=constantCorrect answer is option 'D'. Can you explain this answer?
Question Description
If ∫(sin 2x - cos 2x)dx = (1/√2) sin (2x-a) + ba)a=(π/4), b=0b)a=-(π/4), b=0c)a=(5π/4), b=constantd)a=-(5π/4), b=constantCorrect answer is option 'D'. 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 If ∫(sin 2x - cos 2x)dx = (1/√2) sin (2x-a) + ba)a=(π/4), b=0b)a=-(π/4), b=0c)a=(5π/4), b=constantd)a=-(5π/4), b=constantCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If ∫(sin 2x - cos 2x)dx = (1/√2) sin (2x-a) + ba)a=(π/4), b=0b)a=-(π/4), b=0c)a=(5π/4), b=constantd)a=-(5π/4), b=constantCorrect answer is option 'D'. Can you explain this answer?.
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