{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture31hout

# lecture31hout - MATH 006 Calculus and Linear...

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

MATH 006 Calculus and Linear Algebra (Lecture 31) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 11

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

View Full Document
Outline 1 Method of Substitution 2 Finding the Right Substitution 3 Examples Albert Ku (HKUST) MATH 006 2 / 11
Method of Substitution Method of Substitution Example Find each of the following indefinite integrals: (a) x 10 dx (b) (3 x + 2) 10 dx Solution (a) x 10 dx = x 11 11 + C (b) What is (3 x + 2) 10 dx ? The indefinite integral will be much simpler if (3 x + 2) can be replaced by a new variable u . This can be done by the method of subsitution . Albert Ku (HKUST) MATH 006 3 / 11

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

View Full Document
Method of Substitution The method of substitution is as follows: Let u be a new variable which is equal to an expression in x . In the example, we set u = 3 x + 2. Differentiate u with respect to x i.e. du dx = 3. Then we rewrite it formally as dx = 1 3 du Substitute 3 x + 2 by u and dx by 1 3 du in the indefinite integral. We get (3 x + 2) 10 dx = u 10 1 3 du = 1 3 u 10 du Albert Ku (HKUST) MATH 006 4 / 11
Method of Substitution Find the indefinite integral in terms of u : 1 3 u 10

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.

{[ snackBarMessage ]}

### Page1 / 11

lecture31hout - MATH 006 Calculus and Linear...

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

View Full Document
Ask a homework question - tutors are online