Question

integral question:

find the area of the shaded region in the diagram below.

Answer 1

The answer seems to be 0 :/

Answer 2

thats what i got lol

Answer 3

but its not possible lol i dnt no what im doing wrong

Answer 4

That's what I thought too! It doesn't seem to be possible! I'll keep trying.

Answer 5

my answer is 1

Answer 6

The answer is -2+2sqrt(2), but since area cannot be negative, it's just 2+2sqrt(2)

Answer 7

i integrated from 0 to pi/2 for cosx - sinx

Answer 8

the answer is \[(2-\sqrt{2})u ^{2}\]

Answer 9

@urbanderivative: That's what I did too initially. You get 0 for that because after integration you get [sin x+cos x]

Answer 10

yea ur right

Answer 11

so how did they do it?

Answer 12

what did u do

Answer 13

@and: Where did the "u" come from?

Answer 14

lol what do u mean

Answer 15

In the answer "(2-sqrt(2))u^2) where did "u" come from? It isn't in the equation! And if you're using limits, there shouldn't be a variable in the final answer..

Answer 16

the u is units squared because its area

Answer 17

Oh. Thanks! And I'm sorry, I'm still getting 2+sqrt(2)

Answer 18

omg kill me lol thats close though im not even getting close to that what did you do to get that answer

Answer 19

But the idea is that you can't integrate the entire area directly. You have to integrate from the point of intersection and double it. It's the basic rule of integration, and all of us forgot!

Answer 20

oh lol ill have a go at it again thanks for your help

Answer 21

You're welcome. I'll recheck and let you know if I figure out where I'm going wrong!

Answer 22

-2+2sqrt(2) was right, except its 2sqrt(2) - 2

Answer 23

2 times the integral 0 to pi/4 for (cosx - sinx) dx.
because pi/4 is the intersection.

Answer 24

@urbanderivative: You're absolutely right! That was such a silly mistake!

Answer 25

it was a team effort.

Answer 26

Interesting thread, but what I found was that the diagram is both not to scale and misleading. The shaded area is the sum of integral of sin from 0 to pi/4 and integral of cos from pi/4 to pi/2

Answer 27

sorry bout that couldn't scan the actual picture into the comp. but thank you for claryifying.