5.4 Indefinite Integrals and the Net Change Theorem/17: Difference between revisions

From Burton Tech. Points Wiki
Jump to navigation Jump to search
No edit summary
m (Protected "5.4 Indefinite Integrals and the Net Change Theorem/17" ([Edit=Allow only administrators] (indefinite) [Move=Allow only administrators] (indefinite)))
 
(31 intermediate revisions by 2 users not shown)
Line 1: Line 1:
17)<math>\int_{}^{}1+tan^2xdx</math> =
<math>
<math>\int_{}^{}1+\frac{sin^2x}{cos^2x}dx</math> =  
\int(1+\tan^2{\alpha})\,d\alpha = \int\sec^2\alpha \,d\alpha = \tan\alpha + C
<math>\int_{}^{}\frac{cos^2x+sin^2x}{cos^2x}dx</math>
</math>




[[5.3 The Fundamental Theorem of Calculus/1|1]]
Note: <math>1+\tan^2{\alpha} = \sec^2\alpha</math>
[[5.3 The Fundamental Theorem of Calculus/3|3]]
 
[[5.3 The Fundamental Theorem of Calculus/5|5]]
 
[[5.3 The Fundamental Theorem of Calculus/7|7]]
Or,
[[5.3 The Fundamental Theorem of Calculus/8|8]]
 
[[5.3 The Fundamental Theorem of Calculus/9|9]]
 
[[5.3 The Fundamental Theorem of Calculus/10|10]]
<math>
[[5.3 The Fundamental Theorem of Calculus/11|11]]
 
[[5.3 The Fundamental Theorem of Calculus/13|13]]
\int(1+\tan^2{\alpha})\,d\alpha = \int\left(1+\frac{sin^2\alpha}{cos^2\alpha}\right)d\alpha = \int\left(\frac{cos^2\alpha+sin^2\alpha}{cos^2\alpha}\right)d\alpha  = \int\frac{1}{cos^2\alpha}\,d\alpha =
[[5.3 The Fundamental Theorem of Calculus/15|15]]
 
[[5.3 The Fundamental Theorem of Calculus/17|17]]
\int\sec^2\alpha \,d\alpha = \tan{\alpha}+C
[[5.3 The Fundamental Theorem of Calculus/19|19]]
</math>
[[5.3 The Fundamental Theorem of Calculus/20|20]]
 
[[5.3 The Fundamental Theorem of Calculus/21|21]]
 
[[5.3 The Fundamental Theorem of Calculus/23|23]]
Note: <math>\cos^2\alpha+sin^2\alpha=1</math>
[[5.3 The Fundamental Theorem of Calculus/25|25]]
[[5.3 The Fundamental Theorem of Calculus/27|27]]
[[5.3 The Fundamental Theorem of Calculus/28|28]]
[[5.3 The Fundamental Theorem of Calculus/29|29]]
[[5.3 The Fundamental Theorem of Calculus/31|31]]
[[5.3 The Fundamental Theorem of Calculus/33|33]]
[[5.3 The Fundamental Theorem of Calculus/35|35]]
[[5.3 The Fundamental Theorem of Calculus/37|37]]
[[5.3 The Fundamental Theorem of Calculus/39|39]]
[[5.3 The Fundamental Theorem of Calculus/41|41]]
[[5.3 The Fundamental Theorem of Calculus/53|53]]

Latest revision as of 19:39, 21 September 2022


Note:


Or,



Note:

Retrieved from "https://wiki.btechp.org/index.php?title=5.4_Indefinite_Integrals_and_the_Net_Change_Theorem/17&oldid=4656"