Some AP Calc BC Formulas

18 flashcards · Mathematics · by andrewgrasman

1. ∫cos⁡(u)du\int\cos(u)du∫cos(u)du

   sin⁡(u)+C\sin(u)+Csin(u)+C

2. ∫sin⁡(u)du \int\sin(u)du ∫sin(u)du

   −cos⁡(u)+C -\cos(u)+C −cos(u)+C

3. ∫sec⁡2(u)du\int\sec^2(u)du∫sec2(u)du

   tan⁡(u)+C\tan(u)+Ctan(u)+C

4. ∫csc⁡2(u)du\int\csc^2(u)du∫csc2(u)du

   −cot⁡(u)+C-\cot(u)+C−cot(u)+C

5. ∫tan⁡usec⁡u du\int\tan u \sec u \space du∫tanusecu du

   sec⁡(u)+C\sec(u)+Csec(u)+C

6. ∫1udu\int\frac{1}{u}du∫u1​du

   ln⁡∣u∣+C\ln|u|+Cln∣u∣+C

7. ∫tan⁡u du\int\tan u \space du∫tanu du

   −ln⁡∣cos⁡(u)∣+C-\ln|\cos(u)|+C−ln∣cos(u)∣+C

8. ∫cot⁡u du\int\cot u \space du∫cotu du

   ln⁡∣sin⁡(u)∣+C\ln|\sin(u)|+Cln∣sin(u)∣+C

9. ∫sec⁡u du\int\sec u \space du∫secu du

   ln⁡∣sec⁡u+tan⁡u∣\ln|\sec u +\tan u |ln∣secu+tanu∣

10. ∫csc⁡u du\int\csc u \space du∫cscu du

    −ln⁡∣sin⁡u∣+C-\ln|\sin u|+C−ln∣sinu∣+C

11. ∫eu du\int e^u\space du∫eu du

    eu du+Ce^u\space du+Ceu du+C

12. ∫au du\int a^u \space du∫au du

    auln⁡a+C\frac{a^u}{\ln a}+Clnaau​+C

13. ∫dua2−u2\int\frac{du}{\sqrt{a^2-u^2}}∫a2−u2 ​du​

    arcsin⁡ua+C\arcsin \frac{u}{a}+Carcsinau​+C

14. ∫duu2+a2\int\frac{du}{u^2+a^2}∫u2+a2du​

    1aarctan⁡ua+C\frac{1}{a}\arctan \frac{u}{a}+Ca1​arctanau​+C

15. ∫duuu2−a2\int\frac{du}{u\sqrt{u^2-a^2}}∫uu2−a2 ​du​

    1aarcsec∣u∣a+C\frac{1}{a} arcsec\frac{|u|}{a}+Ca1​arcseca∣u∣​+C

16. Volume by discs

    V=π∫ab(r(x))2 dxV=\pi\int_{a}^{b}(r(x))^2 \space dxV=π∫ab​(r(x))2 dx

17. Volume by washers

    V=π∫ab((R(x))2−(r(x))2) dxV=\pi\int_{a}^{b}((R(x))^2-(r(x))^2) \space dxV=π∫ab​((R(x))2−(r(x))2) dx

18. Volume by shells

    2π∫abr(x)h(x)dx2\pi \int_{a}^{b} r(x)h(x)dx2π∫ab​r(x)h(x)dx