03 - IndefiniteInt - Indefinite Integral d(sin x = cos x An antiderivative of cos x is sin x since dx But g(x = sin x 2 is also an antiderivative since

# 03 - IndefiniteInt - Indefinite Integral d(sin x = cos x An...

• Notes
• 4

This preview shows page 1 - 4 out of 4 pages.

Indefinite Integral An antiderivative of cos x is sin x since d (sin x ) dx = cos x . But g ( x ) = sin x + 2 is also an antiderivative, since ! g ( x ) = cos x . In general, the set of all antiderivatives of cos x is sin x + C where C is a constant. Definition: The indefinite integral of f , f ( x ) ! , is defined f ( x ) dx = F ( x ) where ! F ( x ) = f ( x ) " . The indefinite integral is a function. Ex. 1 x 2 + 1 dx = ! Ex. t 4 ! t t + 1 t dt = "
Note: on-line quiz problems do not include the “C”. In class we