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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]

Solution Preview

1. Find the indefinite integral for the following functions:
a. f(X) = 10000
∫f(X) = ∫10000 = 10000 X

b. f(X) = 20X
∫f(X) = ∫20x = 10 X2

c. f(X) = 1- X2
∫f(X) = ∫(1- X2) = ∫1 -∫X2 = x - 1/3 *X3

d. f(X) = 5X + X-1
∫f(X) = ∫(5X + X-1) = 5∫x +∫X^-1 = 5/2 x2 + ln X

e. f(X) = 12- 2X
∫f(X) = ∫(12- 2X ) = ∫12 -∫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.

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