The value of $$I=2$$∫$$sin$$⁡xsin⁡$$(x$$−π$$/4)dx$$ is

Correct option is 3x+log⁡|sin⁡(x−π/4)|+C

Questions

The value of $I = \sqrt{2} \int \frac{\sin x}{\sin (x - π / 4)} d x$ is

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x+log⁡|cos⁡(x−π/4)|+C

x−log⁡|sin⁡(x−π/4)|+C

x+log⁡|sin⁡(x−π/4)|+C

x−log⁡|cos⁡(x−π/4)|+C

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detailed solution

Correct option is C

Put x−π/4=tI=2∫sin⁡(π/4+t)sin⁡tdt=∫(cot⁡t+1)dt=t+log⁡|sin⁡t|+C′=x+log⁡|sin⁡(x−π/4)|+C,C=C′+π/4

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The value of I=2∫sin⁡xsin⁡(x−π/4)dx is

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The value of $I = \sqrt{2} \int \frac{\sin x}{\sin (x - π / 4)} d x$ is