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

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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