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Indefinite Integrals

Indefinite Integrals. Objectives. Students will be able to Calculate an indefinite integral. Calculate a definite integral. Definition. The symbol ∫ is the integral sign; f ( x ) is the integrand; x is the variable of integration; and C is the constant of integration.

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Indefinite Integrals

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  1. Indefinite Integrals

  2. Objectives Students will be able to • Calculate an indefinite integral. • Calculate a definite integral.

  3. Definition The symbol ∫is the integral sign; f(x) is the integrand; x is the variable of integration; and C is the constant of integration.

  4. Important Integrals

  5. General Rules of Integration where a is a constant

  6. Example 1 Evaluate the indefinite integral

  7. Example 2 Evaluate the indefinite integral

  8. Example 3 Evaluate the indefinite integral

  9. Example 4 Evaluate the indefinite integral

  10. Example 5 Evaluate the indefinite integral

  11. Example 6 Evaluate the indefinite integral

  12. Example 7 Evaluate the indefinite integral

  13. Example 8 Under certain conditions, the number of diseased cells N(t) at time t increases at a rate where A is the rate of increase at time 0 (in cells per day) and k is a constant. a. Suppose A = 60, and at 4 days, the cells are growing at a rate of 300 per day. Find a formula for the number of cells after t days, given that 400 cells are present at t = 0. b. Use your answer from part a to find the number of cells present after 11 days.

  14. Example 9 Suppose v(0)= –7, and s(0) = 12. Find s(t).

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