AP Calculus Unit 6 Terms

Terms from unit 6.6-6.10 in AP Calculus

∫sinx

−cosx+C

∫cosx

sinx+C

x^n antiderivative power rule

n^x+1 / n+1

Fundamental Theorem of Calculus

∫ab​ f(x) = F(b)−F(a) (from integral a to b of s function, minus the top by the bottom)

∫e^x

e^x +c

∫a^x

a^x / ln a +c

∫ 1/x

ln |x| +c

sec²x

tanx +C

(csc(x))(cot(x))

-csc(x) + c

(sec(x))(tan(x))

Sec(x) +C

csc² (x)

-cot(x) +C

Along the sin & cos ladder, do you go up or down for antiderivatives?

Up

ln |1| =

0

d/dx sin^-1

1/ square root of 1-x²

d/dx sec^-1

1 / |x| square root of x² -1

d/dx tan^-1

1/ x² +1

When you can do chain rule on an integral, what do you use?

U-substitution

Unless your finding the particular solution, what do you add at the end of an indefinite integral answer?

+C

What types of trig integrals are negative?

Those that start with “c” (cos,csc cot)