Section 5.4 Indefinite Integrals

Flashcards about indefinite integrals

Indefinite Integral

An antiderivative of f. It represents an entire family of functions, one antiderivative for each value of the constant C.

Definite Integral

A number.

Indefinite Integral

A function or family of functions.

How can any indefinite integral formula be verified?

By differentiating the function on the right side and obtaining the integrand.

How is the most general antiderivative on a given interval obtained?

Adding a constant to a particular antiderivative.

When is a formula for a general indefinite integral valid?

Valid only on an interval.

Find the general indefinite integral a)

( )( )  u + 4 2u +1 du

Find the general indefinite integral b)

 + + dx x 1 x x

Evaluate the integral c)

( )( )  + + 3 0 u 4 2u 1 du

Evaluate the integral d)

 4 + + 1 1 dx x x x

Evaluate the integral a)

 −     + − 0 2 4 3 4 1 2 1 x x x dx

Evaluate the integral b)

     − 2 1 2 3 1 4 dx x x

Evaluate the integral c)

     − 8 1 2 8 dx x x

Evaluate the integral d)

( )  + 1 0 3 x 3 dx x

Evaluate the integral e)

( )  + 
0 4e 5sin x dx x

Evaluate the integral f)

x  4 0 sec tan 
  d

Evaluate the integral g)

 + 4 0 2 2 cos 4 5cos 


 d

Evaluate the integral h)

( )  + 1 0 3 4 x 4 x 5 x dx

Evaluate the integral i)

 − − 3 1 0 4 2 1 1 dx x x