R is the first quadrant region enclosed by the x-axis, the curve y = 2x + b, and the line x = b, where b 0. Find the value of b so that the area of the region R is 288 square units.

Question

R is the first quadrant region enclosed by the x-axis, the curve y = 2x + b, and the line x = b, where b > 0. Find the value of b so that the area of the region R is 288 square units.

anonymous · Answer

the farthest i got was the integral from something to b of 2x+b

zepdrix · Answer

|dw:1461632906988:dw|When I first looked at this, I thought we would be integrating with these boundaries (the dots I made).
But it appears they made things a little easier for us.
Our region R is only in the first quadrant.

zepdrix · Answer

So your "something" is simply x=0.

zepdrix · Answer

$$\large\rm \int\limits_0^b 2x+b~dx=288$$Solve for b.

anonymous · Answer

and since b is a constant it goes out front..

anonymous · Answer

no wait thats wrong

zepdrix · Answer

Ya, don't try to pull anything out front.
Won't work out nicely :)

Just power rule and stuff.

anonymous · Answer

oh god, well im getting b^2+b^2=288,

zepdrix · Answer

Good good good.

anonymous · Answer

2b^2

anonymous · Answer

12

anonymous · Answer

i geuss i just didnt get that relation of x=0 tok fresh eyes to see it TY

zepdrix · Answer

b=12, yay good job \c:/