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Provide solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.8 question 26

Answers (1)

Amswer:

        \frac{1}{2}log\left | 6cos\, x+4sin\, x \right |+C

Hint:

        \int \! \frac{1}{t}dt=log\left | t \right |+C

Given:

        \int \! \frac{2cos\, x-3sin\, x}{6cos\, x+4sin\, x}dx                        ......(1)

Explanation:

Let

        6cos\, x+4sin\, x=t

        (-6sin\, x+4cos\, x)dx=dt

        2(2cos\, x-3sin\, x)dx=dt

Put in (1)

        \int \! \frac{dt}{2t}

        \frac{1}{2}\int \! \frac{dt}{t}=\frac{1}{2}log\left | t \right |+C

                       =\frac{1}{2}log\left | 6cos\, x+4sin\, x \right |+C

Posted by

Gurleen Kaur

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