- #1
karush
Gold Member
MHB
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$\tiny\text{LCC 206 {review 7r13} Integral substitution}$
$$I=\int_{0}^{\pi/4}
\cos^5\left({2x}\right)\sin^2 \left({2x}\right)\,dx= \frac{4}{105} $$
$\text{u substitution } $
\begin{align}\displaystyle
u& = 2x&
du&= 2 \ d{x}&
2(\pi/4) &=\pi/2
\end{align}
$\text{then } $
$$I=2\int_{0}^{\pi/2}
\cos^5\left({u}\right)\sin^2 \left({u}\right)\,du
\implies \int_{0}^{\pi/2}
{\left(\cos^2 \left({u}\right)\right)}^{2}
\sin^2 \left({u}\right)\cos\left({u}\right) \ dx $$
$\text{Not sure if this is a good direction to go in?} $
$\tiny\text{ Surf the Nations math study group}$
![Person surfing :person_surfing: 🏄](https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f3c4.png)
$$I=\int_{0}^{\pi/4}
\cos^5\left({2x}\right)\sin^2 \left({2x}\right)\,dx= \frac{4}{105} $$
$\text{u substitution } $
\begin{align}\displaystyle
u& = 2x&
du&= 2 \ d{x}&
2(\pi/4) &=\pi/2
\end{align}
$\text{then } $
$$I=2\int_{0}^{\pi/2}
\cos^5\left({u}\right)\sin^2 \left({u}\right)\,du
\implies \int_{0}^{\pi/2}
{\left(\cos^2 \left({u}\right)\right)}^{2}
\sin^2 \left({u}\right)\cos\left({u}\right) \ dx $$
$\text{Not sure if this is a good direction to go in?} $
$\tiny\text{ Surf the Nations math study group}$
![Person surfing :person_surfing: 🏄](https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f3c4.png)
![Person surfing :person_surfing: 🏄](https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f3c4.png)
![Person surfing :person_surfing: 🏄](https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f3c4.png)
![Person surfing :person_surfing: 🏄](https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f3c4.png)
![Person surfing :person_surfing: 🏄](https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f3c4.png)