rules of integration

Rules of IntegrationExponential and Trigonometric

Function

• ... finding an Integral is the reverse of finding a Derivative.

• (So you should really know about Derivatives )• Like here:• Example: What is an integral of 2x?

• We know that the derivative of x2 is 2x ...

• ... so an integral of 2x is x2

Rules of Integration in Exponential Function

1.

2.

3.

Remember the three General rules for Integration

1.

2.

3.

Examples:

1. Integrate

2. Integrate .

3. Integrate

u-substitution u = -x du = -1 dx-1 du = dx

Example:

Integrate

Example: Integrate

Examples:

Integrate

Examples:

Integrateu-substitution u = 2x+3 du = 2 dx(1/2) du = dx

Rules of Integration in Trigonometric Function

Trigonometric Functions

A.

B.

C.

D.

C.

D.

E.

F.

G.

H.

I.

Rules of Differentiation

Indefinite Integrals

Indefinite integrals result from trigonometric identities and u-

substitution

Examples

A. Integrate

u-substitution

u = 3x

du = 3dx

(1/3) du = dx

Recall

B. Integrate

Examples

u-substitution

u = 5x

du = 5dx

(1/5) du = dx

Recall

C. Integrate

Examples u-substitution

u = 4x

du = 4dx

(1/4) du = dx

Recall

D. Integrate

Examples

Trigonometric Functions

A.

B.

C.

D.

C.

D.

E.

F.

G.

H.

I.

D. Integrate

Examples

Indefinite Integrals

D. Integrate

Examplesu-substitution

u = sin x

du = cos x dx

Rules of Differentiation

D. Integrate

Examplesu-substitution

u = sin x

du = cos x dx

E. Integrate

Examples

Trigonometric Functions

A.

B.

C.

D.

C.

D.

E.

F.

G.

H.

I.

E. Integrate

Examples u-substitution

u = 10x

du = 10dx

(1/10)du = dx

F. Integrate Example

u-substitution

u = sin x

du = cos dx

Recall

INTEGRATE THE FOLLOWING1.

u-substitution u-substitution

Thank You and

God Bless