{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Evaluating

# Evaluating - EVALUATING DEFINITE INTEGRALS Although we...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: EVALUATING DEFINITE INTEGRALS Although we could calculate some definite integrals, it was quite tedious and time-consuming. Sir Issac Newton, the creator of Calculus, found a much simpler way to evaluate definite integrals by using antiderivatives. It consists of two different theorems, namely the Fundamental Theorem of Calculus part 1 and 2. We start with the second part Theorem 1 (The Fundamental Theorem of Calculus 2 (Evaluation Theorem)) . If f is a continuous on the interval [ a,b ] , then Z b a f ( x ) dx = F ( b )- F ( a ) where F is any antiderivative of f , that is, F = f . Proof. We divide the interval [ a,b ] into n subintervals with endpoints x = a,x 1 ,x 2 , ··· , x n = b and with length Δ x = ( b- a ) /n . Let F be any antiderivative of f . We can express the total difference in the F values as the sum of the differences over subintervals: F ( b )- F ( a ) = F ( x n )- F ( x ) = [ F ( x n )- F ( x n- 1 )] + [ F ( x n- 1 ) + F ( x n- 2 )] + ··· + [ F ( x 1 )- F ( x )]...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

Evaluating - EVALUATING DEFINITE INTEGRALS Although we...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online