5 Steps to a 5 AP Calculus BC 2019

208 STEP 4. Review the Knowledge You Need to Score High

10.1 Evaluating Basic Integrals

Main Concepts:Antiderivatives and Integration Formulas, Evaluating Integrals

TIP • Answer all parts of a question from Section II even if you think your answer to an earlier

part of the question might not be correct. Also, if you do not know the answer to part

one of a question, and you need it to answer part two, just make it up and continue.

Antiderivatives and Integration Formulas

Definition:A functionF is an antiderivative of another functionf ifF′(x)=f(x) for all

xin some open interval. Any two antiderivatives off differ by an additive constantC.We

denote the set of antiderivatives off by

∫

f(x)dx, called the indefinite integral of f.

Integration Rules:

1.

∫

f(x)dx=F(x)+C⇔F′(x)=f(x)

2.

∫

af(x)dx=a

∫

f(x)dx

3.

∫

−f(x)dx=−

∫

f(x)dx

4.

∫

[f(x)±g(x)]dx=

∫

f(x)dx±

∫

g(x)dx

Differentiation Formulas: Integration Formulas:

1.

d

dx

(x)= 11.

∫

1 dx=x+C

2.

d

dx

(ax)=a 2.

∫

adx=ax+C

3.

d

dx

(xn)=nxn−^1 3.

∫

xndx=

xn+^1

n+ 1

+C,n=−/ 1

4.

d

dx

(cosx)=−sinx 4.

∫

sinxdx=−cosx+C

5.

d

dx

(sinx)=cosx 5.

∫

cosxdx=sinx+C

6.

d

dx

(tanx)=sec^2 x 6.

∫

sec^2 xdx=tanx+C

7.

d

dx

(cotx)=−csc^2 x 7.

∫

csc^2 xdx=−cotx+C

8.

d

dx

(secx)=secx tanx 8.

∫

secx(tanx)dx=secx+C

9.

d

dx

(cscx)=−cscx(cotx)9.

∫

cscx(cotx)dx=−cscx+C