Indefinite Integrals. Objectives Students will be able to Calculate an indefinite integral. Calculate a definite integral.

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Presentation transcript:

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.

Important Integrals

General Rules of Integration where a is a constant

Example 1 Evaluate the indefinite integral

Example 2 Evaluate the indefinite integral

Example 3 Evaluate the indefinite integral

Example 4 Evaluate the indefinite integral

Example 5 Evaluate the indefinite integral

Example 6 Evaluate the indefinite integral

Example 7 Evaluate the indefinite integral

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.

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