Warm Up. 7.1 A – Initial Value Problems Consider: then: or It doesn’t matter whether the constant was 3 or -5, since when we take the derivative the.

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Presentation transcript:

Warm Up

7.1 A – Initial Value Problems

Consider: then: or It doesn’t matter whether the constant was 3 or -5, since when we take the derivative the constant disappears. However, when we try to reverse the operation: Given: find We don’t know what the constant is, so we put “C” in the answer to remind us that there might have been a constant. Think about it….

Integrals such as are called definite integrals because we can find a definite value for the answer. The constant always cancels when finding a definite integral, so we leave it out! So far, we have found definite integrals.

Integrals such as are called indefinite integrals because we can not find a definite value for the answer. When finding indefinite integrals, we always include the “plus C”. Indefinite Integrals

Common antiderivatives YOU NEED TO KNOW

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Examples

More Examples

Initial Value Problems We cannot find C unless additional information is given. All we need is a single point, called an initial condition. A problem with an initial condition is called a initial value problem.

Example

Find the position function for v(t) = t 3 - 2t 2 + t s(0) = 1 C = 1

Homework