Math, asked by sumitkumar5060666, 5 months ago

13.
समाकलन करें
741 : (sin 3x.cos 6x dx.
Integrate : ſsin 3x.cos 6x dx .​

Answers

Answered by MaheswariS
2

\underline{\textsf{To find:}}

\mathsf{\displaystyle\int\,sin3x\,cos6x\;dx}

\underline{\textsf{Solution:}}

\textsf{Consider,}

\textsf{We apply decomposition method to solve the given integral}

\mathsf{\displaystyle\int\,sin3x\,cos6x\;dx}

\textsf{This can be written as}

\mathsf{=\displaystyle\dfrac{1}{2}\int\,2\,sin3x\,cos6x\;dx}

\textsf{Using the identity,}

\boxed{\mathsf{sin(A+B)+sin(A-B)=2\,sinA\,cosB}}

\mathsf{=\displaystyle\dfrac{1}{2}\int\,[sin(3x+6x)+sin(3x-6x)]\;dx}

\mathsf{=\displaystyle\dfrac{1}{2}\int\,[sin9x+sin(-3x)]\;dx}

\mathsf{=\displaystyle\dfrac{1}{2}\int\,[sin9x-sin3x]\;dx}

\mathsf{=\displaystyle\dfrac{1}{2}[\dfrac{-cos9x}{9}-(\dfrac{-cos3x}{3})]+C}

\mathsf{=\displaystyle\dfrac{1}{2}[\dfrac{-cos9x}{9}+\dfrac{cos3x}{3}]+C}

\underline{\textsf{Answer:}}

\mathsf{\displaystyle\int\,sin3x\,cos6x\;dx=\displaystyle\dfrac{1}{2}[\dfrac{-cos9x}{9}+\dfrac{cos3x}{3}]+C}

Find more:

Integrate of e^x sec x(1+tanx) dx

https://brainly.in/question/6040969

Integration of sin6x/sin10x sin4x

https://brainly.in/question/24749414

Integrate cotx/cuberoot of sinx dx

https://brainly.in/question/15962952

Similar questions