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two curves have equations y=x^2-4x+7 and y=6x-x^2-1. Find the area between the two curves

 Feb 10, 2017

Best Answer 

 #1
avatar+26398 
+20

two curves have equations y=x^2-4x+7 and y=6x-x^2-1.

Find the area between the two curves

 

f(x)=6xx21g(x)=x24x+7

 

intersections:

g(x)=f(x)x24x+7=6xx212x210x+8=0|:2x25x+4=0(x1)(x4)=0x1=1andx2=4

 

area between the two curves:

41( f(x)g(x) ) dx=41( 6xx21(x24x+7) ) dx=41( 6xx21x2+4x7 ) dx=41( 10x2x28 ) dx=[ 10x222x338x ]41=[ 5x223x38x ]41=[ 5(4)223(4)384 ][ 5(1)223(1)381 ]=5162364325+23+8=512364+23=5123(641)=5123(63)=51221=9

 

The area between the two curves is 9

 

laugh

 Feb 10, 2017
 #1
avatar+26398 
+20
Best Answer

two curves have equations y=x^2-4x+7 and y=6x-x^2-1.

Find the area between the two curves

 

f(x)=6xx21g(x)=x24x+7

 

intersections:

g(x)=f(x)x24x+7=6xx212x210x+8=0|:2x25x+4=0(x1)(x4)=0x1=1andx2=4

 

area between the two curves:

41( f(x)g(x) ) dx=41( 6xx21(x24x+7) ) dx=41( 6xx21x2+4x7 ) dx=41( 10x2x28 ) dx=[ 10x222x338x ]41=[ 5x223x38x ]41=[ 5(4)223(4)384 ][ 5(1)223(1)381 ]=5162364325+23+8=512364+23=5123(641)=5123(63)=51221=9

 

The area between the two curves is 9

 

laugh

heureka Feb 10, 2017

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