Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents
, and find the area using high school geometry.
(0 → 4) ∫|2x−5|dx
(0 → 4) ∫|2x−5|dx
1 answer:
Answer:
17/2
Step-by-step explanation:
The graph of the given absolute funciton |2xd-5| is attached below
Find the area of each triangle using the graph
Take the area from x=0 to 4
break the graph into two right angle triangle
Area of the triangle = 1/2 times base times height
Green triangle x=2.5 to 4
base = 3/2 and height = 3
Area of green part =
Red triangle x=0 to 2.5
base = 5/2 and height = 5
Area of red part =
Total area=
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Answer:
1. Perpendicular
2. Isosceles
3. Never
Step-by-step explanation:
1. AC ⊥ BD because diameter of a square are perpendicular bisector of each other.
2. In Δ AOB , By using pythagoras : AB² = OA² + OB² .......( 1 )
In Δ COB , By using pythagoras : BC² = OC² + OB² ..........( 2 )
But, OA = OC because both are radius of same circle
So, by using equations ( 1 ) and ( 2 ), We get AB = BC ≠ AC
⇒ ABC is a triangle having two equal sides so ABC is an isosceles triangle.
3. The side can never be equal to radius of circle because the side of the square will be chord for the circle and in a circle chord can never be equal to its radius
