How to do this integration question? (1 Viewer)

[astroman]

 

[hypermax]

split the areas up, the first one the triangle doesn't need integration, use the area of circle for both semi circles or you can just combine the 2 semi circles together cause they have the same radius and just use the area of a circle formula

 

[astroman]

whats the difference between part a and b?

 

[hypermax]

i really see nothing different, question number one is the equation for number 2

 

[astroman]

wait so u do u integrate then for the semi-circle?

 

[hypermax]

wait so u do u integrate then for the semi-circle?

why? Isn't the question asking for the area, since its a semi-circle, why can't you use the area of a circle formula to find out the area

 

[hypermax]

I think the question was designed so that you notice integration isn't always necessary when finding the areas of shapes found in the graph

 

[astroman]

uhh im confused can u show working for part 1

 

[Ekman]

As a matter of fact, part a and part b are too separate questions that may look similar but are different. Part a only refers to value not area, as you know integrating a function doesn't necessarily gives you the area. Its only the net area it gives you. Thus part a is asking for net area and part b is asking for total area.
Since the area under the curve is negative, its 'negative' when calculating part a but 'positive' when calculating part b

 

[astroman]

As a matter of fact, part a and part b are too separate questions that may look similar but are different. Part a only refers to value not area, as you know integrating a function doesn't necessarily gives you the area. Its only the net area it gives you. Thus part a is asking for net area and part b is asking for total area.

whats the difference?

 

[Ekman]

whats the difference?

Net area factors in the area under the curve as negative, but total area factors in the area both above and below the axis as positive

 

[astroman]

is part a 16?

 

[Ekman]

Part a) 0.5 * 2 * 3 + 0.5* 2* 1 - pi*1*0.5 + pi* 1 * 0.5

Part b) 0.5 * 2 * 3 + 0.5* 2* 1 + pi*1*0.5 + pi* 1 * 0.5

 

[astroman]

y did u minus in part a?

 

[Silly Sausage]

Definite integration is not restricted purely to finding the area/volume under a function. Part a just wants you to evaluate the definite integral whilst part b wants you to find the area. To find the area of a semi-circle you use the formula

y did u minus in part a?

 

[astroman]

can i see working plz, this is frustrating me

 

[Ekman]

can i see working plz, this is frustrating me

Im being serious, that's all I can show for the working out. Its the logic behind integrals that you have to understand. Silly Sausage explained it perfectly.

 

[astroman]

is b) 7.14

 

[Ekman]

is b) 7.14

Just look at my previous post.

 

[InteGrand]

For part a) you basically ignore the semi-circles since they cancel each other out.