Crazy Areas 2

Calculus Level 4

Find the area of the region bounded by the following curves

x + y < 6 x+y<6

x 2 + y 2 < 6 y x^2+y^2<6y

y 2 < 8 x y^2<8x

If your answer can be expressed as a π + b a\pi + b .

where a a and b b are real numbers.

Calculate the value of a b ab .


The answer is -0.375.

Prakhar Bindal by Prakhar Bindal , 22, India

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2 solutions

Prakhar Bindal
Oct 17, 2016

I Am attaching my solution

3 Helpful 0 Interesting 0 Brilliant 0 Confused

@Brian Charlesworth

sir you also did it like this??

Prakhar Bindal - 4 years, 8 months ago

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Yes, exactly the same way. :)

Brian Charlesworth - 4 years, 8 months ago

i have a different method ! will upload it soon !

A Former Brilliant Member - 4 years, 7 months ago

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see my sol . @Prakhar Bindal

A Former Brilliant Member - 4 years, 7 months ago

Did the same way

Samarth Agarwal - 4 years, 8 months ago

bro help here https://brilliant.org/discussions/thread/little-help/

A Former Brilliant Member - 4 years, 7 months ago

i did it without integration, pure geometry solution, so here it goes ! cut that required area OBDO(see bro's pic) in 2 parts and then instead of going with the same old integration , draw a box circumscribing the circle the box cuts the quadrants in 4 equal parts , u just wana calculate the one of these , so,, ans will be ar(box-circle quadrant)/4 and u get it . i thought of it as i forgot the integration formula ! :P

0 Helpful 0 Interesting 0 Brilliant 0 Confused

think in the box and not out of it ! :P

A Former Brilliant Member - 4 years, 7 months ago

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