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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Fundamental Integration

  • question_answer
    \[\int_{{}}^{{}}{(3\,\text{cose}{{\text{c}}^{2}}x+2\sin 3x)\ dx=}\] [AI CBSE 1981]

    A)            \[3\cot x+\frac{2}{3}\cos 3x+c\]      

    B)            \[-\left( 3\cot x+\frac{2}{3}\cos 3x \right)+c\]

    C)            \[3\cot x-\frac{2}{3}\cos 3x+c\]

    D)            None of these

    Correct Answer: B

    Solution :

               \[\int_{{}}^{{}}{(3\text{cose}{{\text{c}}^{\text{2}}}x+2\sin 3x)\,dx}\]            \[=-3\cot x-\frac{2\cos 3x}{3}+c=-\,[3\cot x+\frac{2}{3}\cos 3x]+c.\]


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