This document discusses integration and antiderivatives. It explains that the antiderivative of a function is the original equation found by taking the derivative. It provides the procedure for finding antiderivatives by adding one to the exponent, dividing the coefficient by the new exponent, and adding + c. The document also describes the substitution method for integrals involving quantities raised to powers, trigonometric ratios, or unusual angles. Finally, it discusses position, velocity, and acceleration and how derivatives relate to instantaneous rates of change.

1. Integration
Group 1

2. • The anti-derivative of a function

b
a
dxxf )(

3. Antiderivative

4. • The original equation found from
the derivative
F(x)

5. Procedure of antiderivatives

6. • Add one to the exponent
• Divide coefficient by new exponent
• Add + c

7. Substitution method(U-sub)

8. • When you:
▫ Have a quantity raised to a power
▫ Have a trigonometric ratio or unusual angles
▫ Have a trigonometric ratio raised to a power
92
)13( x
)3sin( x
)2(csc7
x

9. Position, velocity, acceleration

10. • Position s(t)
• Velocity v(t)
▫ Average:
▫ Instantaneous: s’(t) (derivative)
• Acceleration a(t)
▫ Average:
▫ Instantaneous: v’(t) or s’’(t)
12
12
tt
pp


12
12
tt
vv

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