lecture32

# lecture32 - Lecture 32 1 Lecture 32(Sec 6.2 and 6.3...

This preview shows pages 1–6. Sign up to view the full content.

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

View Full Document

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

View Full Document

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: Lecture 32 1 Lecture 32: (Sec. 6.2 and 6.3) Integration by Substitution, Part II Recall the following results: Let f be a function of u , where u is a differentiable function of x . Then if F is an antiderivative of f ( u ), integraldisplay f ( u ) du dx dx = Integration by Substitution with exponential and log- arithmic functions. We have two more rules of substitution: I. Integrals of Exponential Functions ex. integraldisplay e 3- 4 x dx = Lecture 32 2 ex. integraldisplay e 2 x (1- e 2 x ) 2 dx Lecture 32 3 II. Integrals involving Logarithmic Func- tions integraldisplay 1 x dx = integraldisplay 1 u du dx dx = ex. integraldisplay 2 x 2- 4 x 3- 6 x + 3 dx = Lecture 32 4 Integrals involving ln x ex. integraldisplay ln x x dx = ex. integraldisplay 1 x ln x dx = Lecture 32 5 (Sec. 6.3, Part I) Area and the Definite Integral; The Fun- damental Theorem of Calculus How to find the area under the graph of f on the interval [ a, b ] or from a to b ?...
View Full Document

{[ snackBarMessage ]}

### Page1 / 12

lecture32 - Lecture 32 1 Lecture 32(Sec 6.2 and 6.3...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online