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1 year ago

Find the area between the two functions

Mathematics

1 answer:

Inga [223]1 year ago

5 0

The area between the two functions is 0

<h3>How to determine the area?</h3>

The functions are given as:

f₁(x)= 1

f₂(x) = |x - 2|

x ∈ [0, 4]

The area between the functions is

A = ∫[f₂(x) - f₁(x) ] dx

The above integral becomes

A = ∫|x - 2| - 1 dx (0 to 4)

When the above is integrated, we have:

A = [(|x - 2|(x - 2))/2 - x] (0 to 4)

Expand the above integral

A = [(|4 - 2|(4 - 2))/2 - 4] - [(|0 - 2|(0 - 2))/2 - 0]

This gives

A = [2 - 4] - [-2- 0]

Evaluate the expression

A = 0

Hence, the area between the two functions is 0

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3 years ago

If U = {x: X € N, 1 < × < 15)

Inessa05 [86]

Answer:

Step-by-step explanation:

Given:

U = {x: X € N, 1 < × < 15) = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}

A = {2,4,6,8,10,12,14}

B = {3,6,9,12,15}

C = {5,10,15}

(a) Verify A(BnB)=(AUB)(AUB)

A U (B n B)

= {2,4,6,8,10,12,14} U ( {3,6,9,12,15} n {3,6,9,12,15} )

= {2,4,6,8,10,12,14} U {3,6,9,12,15}

= {2,3,4,6,8,9,10,12,14,15}

( A U B) n (A U B)

= {2,3,4,6,8,9,10,12,14,15} n {2,3,4,6,8,9,10,12,14,15}

= {2,3,4,6,8,9,10,12,14,15}

Therefore

A U (B n B) = ( A U B) n (A U B)

verifies

(b) Verify An(BUC)=(AnB)u(AnC)

A n ( B U C)

= {2,4,6,8,10,12,14} n ( {3,6,9,12,15} U {5,10,15} )

= {2,4,6,8,10,12,14} n {3,5,6,9,10,12,15}

= {6,10,12}

( A n B ) U ( A n C )

= ( {2,4,6,8,10,12,14} n {3,6,9,12,15} ) U ( {2,4,6,8,10,12,14} n {5,10,15} )

= {6,12} U {10}

= {6,10,12}

Therefore

A n ( B U C) = ( A n B ) U ( A n C )

verifies

AU(BUC)

= {2,4,6,8,10,12,14}U{3,6,9,12,15}U{5,10,15}

= {2,3,4,5,6,8,9,10,12,14,15}

(AUB)U(AUC)

= ({2,4,6,8,10,12,14}{3,6,9,12,15})U({2,4,6,8,10,12,14}U{5,10,15})

= {2,3,4,6,8,9,10,12,14,15}U{2,4,5,6,8,10,12,14,15}

= {2,3,4,5,6,8,9,10,12,14,15}

Therefore

AU(BUC)=(AUB)U(AUC)

verifies

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