Notes: `int cos^4(theta) sin(theta) d theta` Evaluate the indefinite integral.

Wednesday, 11 March 2015

$\displaystyle\int{{\cos}}^{{4}}{\left(\theta\right)}{\sin{{\left(\theta\right)}}}{d}\theta$ Evaluate the indefinite integral.

You need to use the following substitution $\displaystyle{\cos{\theta}}={u}$ , such that:

$\displaystyle{\cos{\theta}}={u}\Rightarrow-{\sin{\theta}}{d}\theta={d}{u}\Rightarrow{\sin{\theta}}{d}\theta=-{d}{u}$

$\displaystyle\int{{\cos}}^{{4}}\theta\cdot{\sin{\theta}}{d}\theta=-\int{{u}}^{{4}}{d}{u}$

$\displaystyle-\int{{u}}^{{4}}{d}{u}=-\frac{{{{u}}^{{5}}}}{{5}}+{c}$

Replacing back $\displaystyle{\cos{\theta}}$ for $\displaystyle{u}$ yields:

$\displaystyle\int{{\cos}}^{{4}}\theta\cdot{\sin{\theta}}{d}\theta=-\frac{{{{\left({\cos{\theta}}\right)}}^{{5}}}}{{5}}+{c}$

Hence, evaluating the indefinite integral, yields $\displaystyle\int{{\cos}}^{{4}}\ldots$

You need to use the following substitution $\displaystyle{\cos{\theta}}={u}$ , such that:

$\displaystyle{\cos{\theta}}={u}\Rightarrow-{\sin{\theta}}{d}\theta={d}{u}\Rightarrow{\sin{\theta}}{d}\theta=-{d}{u}$

$\displaystyle\int{{\cos}}^{{4}}\theta\cdot{\sin{\theta}}{d}\theta=-\int{{u}}^{{4}}{d}{u}$

$\displaystyle-\int{{u}}^{{4}}{d}{u}=-\frac{{{{u}}^{{5}}}}{{5}}+{c}$

Replacing back $\displaystyle{\cos{\theta}}$ for $\displaystyle{u}$ yields:

$\displaystyle\int{{\cos}}^{{4}}\theta\cdot{\sin{\theta}}{d}\theta=-\frac{{{{\left({\cos{\theta}}\right)}}^{{5}}}}{{5}}+{c}$

Hence, evaluating the indefinite integral, yields $\displaystyle\int{{\cos}}^{{4}}\theta\cdot{\sin{\theta}}{d}\theta=-\frac{{{{\left({\cos{\theta}}\right)}}^{{5}}}}{{5}}+{c}$

Notes

Wednesday, 11 March 2015

$\displaystyle\int{{\cos}}^{{4}}{\left(\theta\right)}{\sin{{\left(\theta\right)}}}{d}\theta$ Evaluate the indefinite integral.

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Is there any personification in "The Tell-Tale Heart"?

Wednesday, 11 March 2015

Evaluate the indefinite integral.

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Post a Comment

Is there any personification in &quot;The Tell-Tale Heart&quot;?

$\displaystyle\int{{\cos}}^{{4}}{\left(\theta\right)}{\sin{{\left(\theta\right)}}}{d}\theta$ Evaluate the indefinite integral.

Is there any personification in "The Tell-Tale Heart"?