ExamplesExample 1: Evaluate Solution: (Formula 12, applied twice) (Formula 11) (Formula 2) (Arithmetic)
Example 2: Evaluate Solution: (Formula 12) (Formula 11) (Algebra) (Formula 2) (Arithmetic)
Example 3: Find all the antiderivatives of . Solution: This question is just another way to ask that be evaluated. (Formula 12) (Formula 11) (Formulae 2 and 7) (Arithmetic)
Example 4: Evaluate Solution: (Algebra) (Trig Relationships) (Formula 9) Example 5: Evaluate . Solution: (Algebra) (Formula 12) (Formula 11) (Formulae 5 and 6) (Algebra)
Example 6: Suppose . Find the function Solution: (Formula 12) (Formula 11) (Formulae 2 and 6) (Algebra) (Formula 12) (Formula 11) (Formulae 2 and 5) (Algebra) Example 7: Suppose a particle is moving along a line so that the velocity at time t is given by . The displacement at time is zero. Find the displacement at any time t. Solution: (Formula 12) (Formulae 3 and 5) (Algebra) Since , . So .
|