New Notes Blog: `int sin(2x)/sin(x) dx` Find the general indefinite integral.

Tuesday, 23 December 2014

$\displaystyle\int\frac{{\sin{{\left({2}{x}\right)}}}}{{\sin{{\left({x}\right)}}}}{\left.{d}{x}\right.}$ Find the general indefinite integral.

You need to find the indefinite integral, hence, you need to remember that sin $\displaystyle{2}{x}={2}{\sin{{x}}}\cdot{\cos{{x}}}$ , such that:

$\displaystyle\int{\left({\sin{{2}}}{x}\right)}{\left({\sin{{x}}}\right)}{\left.{d}{x}\right.}=\int\frac{{{2}{\sin{{x}}}\cdot{\cos{{x}}}}}{{{\sin{{x}}}}}{\left.{d}{x}\right.}$

$\displaystyle\int{\left({\sin{{2}}}{x}\right)}{\left({\sin{{x}}}\right)}{\left.{d}{x}\right.}=\int{2}{\cos{{x}}}{\left.{d}{x}\right.}={2}\int{\cos{{x}}}{\left.{d}{x}\right.}={2}{\sin{{x}}}+{c}$

Hence, evaluating the indefinite integral, yields $\displaystyle\int{\left({\sin{{2}}}{x}\right)}{\left({\sin{{x}}}\right)}{\left.{d}{x}\right.}={2}{\sin{{x}}}+{c}.$

You need to find the indefinite integral, hence, you need to remember that sin $\displaystyle{2}{x}={2}{\sin{{x}}}\cdot{\cos{{x}}}$ , such that:

$\displaystyle\int{\left({\sin{{2}}}{x}\right)}{\left({\sin{{x}}}\right)}{\left.{d}{x}\right.}=\int\frac{{{2}{\sin{{x}}}\cdot{\cos{{x}}}}}{{{\sin{{x}}}}}{\left.{d}{x}\right.}$

$\displaystyle\int{\left({\sin{{2}}}{x}\right)}{\left({\sin{{x}}}\right)}{\left.{d}{x}\right.}=\int{2}{\cos{{x}}}{\left.{d}{x}\right.}={2}\int{\cos{{x}}}{\left.{d}{x}\right.}={2}{\sin{{x}}}+{c}$

Hence, evaluating the indefinite integral, yields $\displaystyle\int{\left({\sin{{2}}}{x}\right)}{\left({\sin{{x}}}\right)}{\left.{d}{x}\right.}={2}{\sin{{x}}}+{c}.$

New Notes Blog

Tuesday, 23 December 2014

$\displaystyle\int\frac{{\sin{{\left({2}{x}\right)}}}}{{\sin{{\left({x}\right)}}}}{\left.{d}{x}\right.}$ Find the general indefinite integral.

No comments:

Post a Comment

In "By the Waters of Babylon," under the leadership of John, what do you think the Hill People will do with their society?

Tuesday, 23 December 2014

Find the general indefinite integral.

No comments:

Post a Comment

In &quot;By the Waters of Babylon,&quot; under the leadership of John, what do you think the Hill People will do with their society?

$\displaystyle\int\frac{{\sin{{\left({2}{x}\right)}}}}{{\sin{{\left({x}\right)}}}}{\left.{d}{x}\right.}$ Find the general indefinite integral.

In "By the Waters of Babylon," under the leadership of John, what do you think the Hill People will do with their society?