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Question

# I: ∫cos(x−a)sinxdx=cosalog|sinx|+xsina+cII:∫sin(x−a)cos(x−b)dx=cos(b−a)log|sec(x−b)|+xsin(b−a)+c

A
only I is true
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B
only II is true
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C
both I and II are true
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D
neither I nor II are true
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Solution

## The correct option is B both I and II are trueI: ∫cos(x−a)sinxdx=∫cosxcosa+sinxsinasinxdx=cosa∫cotxdx+sina∫dx=cosalog|sinx|+xsina+cII: ∫sin(x−a)cos(x−b)dx =∫sin(x−b+b−a)cos(x−b)dx=∫sin(x−b)cos(b−a)+cos(x−b)sin(b−a)cos(x−b)dx=cos(b−a)∫tan(x−b)dx+sin(b−a)∫dx=cos(b−a)log|sec(x−b)|+xsin(b−a)+c

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