Thread: How do I find the limits of integration?

In a problem such as this:

Sketch the region enclosed by the curves and compute its area as an integral along the x- or y-axis.

y + x = 5,

y - x = 0, y + 3x = 4

or this:

Sketch the region enclosed by the curves and compute its area as an integral along the x- or y-axis.

x = y3 - 18y,

y + 6x = 0
How do I find the limits of integration?

Originally Posted by bigdan

In a problem such as this:

Sketch the region enclosed by the curves and compute its area as an integral along the x- or y-axis.

y + x = 5,

y - x = 0, y + 3x = 4

or this:

Sketch the region enclosed by the curves and compute its area as an integral along the x- or y-axis.

x = y3 - 18y,

y + 6x = 0
How do I find the limits of integration?

first of all, draw your self those lines and you will see limits for integrations ...


to draw any line you need just 2 points and connect them ... (for curves you need at least 3 points)

so ....
so for y = 0 you have x = 5 , and for let's say y = 5 you will have x = 0 so you have 2 points M(5,0) N(0,5) yo you draw the line through those 2 points ... do the same thing with another 2 equations and you will get that region that you need to integrate

to see points of the intersecting, just put first equation in second and see where those 2 lines intersect , same thing with second and third and of course first and third .... and from that you will get your points of integration...

intersecting point of the first and second
put in the second
intersecting first and third
put in the third
and second and third ... x =1



Hint: There are two regions of integration.... calculate both and add them


P.S. second problem do the same way