lecture33hout

lecture33hout - MATH 006 Calculus and Linear Algebra...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 006 Calculus and Linear Algebra (Lecture 33) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 14 Outline 1 Area between two curves 2 An Application - Gini Index Albert Ku (HKUST) MATH 006 2 / 14 Area between two curves Area between two curves Consider the area R bounded by y = g ( x ) and y = f ( x ), where g ( x ) ≥ f ( x ), for a ≤ x ≤ b : R = (area under g ( x ))- (area under f ( x )) = Z b a g ( x ) dx- Z b a f ( x ) dx = Z b a [ g ( x )- f ( x )] dx Albert Ku (HKUST) MATH 006 3 / 14 Area between two curves Example Find the area bounded by y = 6 x- x 2 and y = 0 for 1 ≤ x ≤ 4. Solution Let g ( x ) = 6 x- x 2 and f ( x ) = 0. We need to find the range of values of x such that g ( x ) ≥ f ( x ) i.e. 6 x- x 2 = x (6- x ) ≥ 0. By the following sign chart, g ( x ) ≥ f ( x ) for 0 ≤ x ≤ 6 i.e. the graph of y = 6 x- x 2 always lies above the graph of y = 0 for 1 ≤ x ≤ 4. Therefore, the area is Z 4 1 (6 x- x 2 ) dx = (3 x 2- x 3 3 ) 4 1 = 24 Albert Ku (HKUST) MATH 006 4 / 14 Area between two curves Example Find the area between the graph of y = x 2- 2 x and the x-axis over the interval [- 1 , 1] Solution...
View Full Document

Page1 / 14

lecture33hout - MATH 006 Calculus and Linear Algebra...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online