# Integration Techniques and Applications

1. Find the indefinite integrals for the following functions:

a. f(X) = 10000

b. f(X) = 20X

c. f(X) = 1- X2

d. f(X) = 5X + X-1

e. f(X) = 12- 2X

f. f(X) = X3 + X4

g. f(X) = 200X - X2 + X100

2. Find the definite integral for the following functions:

a. f(X) = 67 over the interval [0,1]

b. f(X) = 30X over the interval [0,2]

c. f(X) = 2- X2 over the interval [2, 4]

d. f(X) = 2- X2 over the interval [3, 4.5]

e. f(X) = 12- 2X over the interval [0, 1]

f. f(X) = X3 + X4 over the interval [0, 3]

g. f(X) = 50X - X2 + X10 over the interval [0, 1]

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#### Solution Preview

1. Find the indefinite integral for the following functions:

a. f(X) = 10000

âˆ«f(X) = âˆ«10000 = 10000 X

b. f(X) = 20X

âˆ«f(X) = âˆ«20x = 10 X2

c. f(X) = 1- X2

âˆ«f(X) = âˆ«(1- X2) = âˆ«1 -âˆ«X2 = x - 1/3 *X3

d. f(X) = 5X + X-1

âˆ«f(X) = âˆ«(5X + X-1) = 5âˆ«x +âˆ«X^-1 = 5/2 x2 + ln X

e. f(X) = 12- 2X

âˆ«f(X) = âˆ«(12- 2X ) = âˆ«12 -âˆ«2x = 12x - X2

f. ...

#### Solution Summary

Fourteen definite and indefinite integrals are solved. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.