5.4 Indefinite Integrals and the Net Change Theorem/37: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
| Line 2: | Line 2: | ||
\begin{align} | \begin{align} | ||
\int_{0}^{\frac{\pi}{4}}\left(\frac{1+\cos^2(\theta)}{\cos^2(\theta)}\right)d\theta &= | \int_{0}^{\frac{\pi}{4}}\left(\frac{1+\cos^2(\theta)}{\cos^2(\theta)}\right)d\theta | ||
&= \int_{0}^{\frac{\pi}{4}}\left(\frac{1}{\cos^2(\theta)} + \frac{\cos^2(\theta)}{\cos^2(\theta)}\right)d\theta | |||
\int_{0}^{\frac{\pi}{4}}\left(\frac{1}{\cos^2(\theta)} + \frac{\cos^2(\theta)}{\cos^2(\theta)}\right)d\theta = \int_{0}^{\frac{\pi}{4}}\sec^2(\theta)} + 1 \\[2ex] | = \int_{0}^{\frac{\pi}{4}}\sec^2(\theta)} + 1 \\[2ex] | ||
& =\tan({\theta}) + \theta \ \bigg|_{0}^{\frac{\pi}{4}}\\[2ex] | & =\tan({\theta}) + \theta \ \bigg|_{0}^{\frac{\pi}{4}}\\[2ex] | ||
Revision as of 15:59, 21 September 2022
Failed to parse (unknown function "\begin{align}"): {\displaystyle \begin{align} \int_{0}^{\frac{\pi}{4}}\left(\frac{1+\cos^2(\theta)}{\cos^2(\theta)}\right)d\theta &= \int_{0}^{\frac{\pi}{4}}\left(\frac{1}{\cos^2(\theta)} + \frac{\cos^2(\theta)}{\cos^2(\theta)}\right)d\theta = \int_{0}^{\frac{\pi}{4}}\sec^2(\theta)} + 1 \\[2ex] & =\tan({\theta}) + \theta \ \bigg|_{0}^{\frac{\pi}{4}}\\[2ex] & =\tan({\frac{\pi}{4}}) + \frac{\pi}{4} \\[2ex] & =1+\frac{\pi}{4} \end{align} }