lecture32

# lecture32 - Math 121 Lecture 32 6.4 Areas in the xy-Plane...

This preview shows pages 1–4. Sign up to view the full content.

§ 6.4 Areas in the xy -Plane Math 121 Lecture 32 ! Properties of Definite Integrals ! Area Between Two Curves ! Finding the Area Between Two Curves

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

View Full Document
y = x 2 – 3 x and the x -axis ( y = 0) from x = 0 to x = 4. Upon sketching the graphs we can see that the two graphs cross; and by setting x 2 – 3 x = 0, we find that they cross when x = 0 and when x = 3. Thus one graph does not always lie above the other from x = 0 to x = 4, so that we cannot directly apply our rule for finding the area between two curves. However, the difficulty is easily surmounted if we break the region into two parts, namely the area from x = 0 to x = 3 and the area from x = 3 to x = 4. For from x = 0 to x = 3, y = 0 is on top; and from x = 3 to x = 4, y = x 2 – 3 x is on top. Consequently, area from x = 0 to x = 3 [ ] = 0 ( ) " x 2 " 3 x ( ) [ ] 0 3 # dx = " x 2 + 3 x ( ) 0 3 # dx = " x 3 3 + 3 x 2 2 # \$ % ( 0 3 = " 9 + 27 2 # \$ % ( " 0 " 0 ( ) = 4.5. Thus the total area is 4.5 + 1.833 = 6.333.

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 / 6

lecture32 - Math 121 Lecture 32 6.4 Areas in the xy-Plane...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online