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Question

The value of 2sinxdxsin(xπ4) is
(where C is constant of integration)

A
x+lncos(xπ4)+C
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B
xlnsin(xπ4)+C
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C
x+lnsin(xπ4)+C
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D
xlncos(xπ4)+C
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Solution

The correct option is C x+lnsin(xπ4)+C
Let I=2sinxdxsin(xπ4)
Put xπ4=t
dx=dt
I=2sin(t+π4)sintdt
I=22(sint+costsint)dt
I=(1+cott)dt
I=t+ln|sint|+c1
I=xπ4+lnsin(xπ4)+c1
I=x+lnsin(xπ4)+C
(where C=c1π4)

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