# Double integral question

## Homework Statement

Consider the integral shown in the sketch. Sketch the region of integration and express the integral with the reverse order of integration and evaluate it leaving your answer in surd form

## The Attempt at a Solution

I shaded the area of integration but I am not sure whether it is the right area. How do I know which area of integration to use? And secondly, when you choose your x limits, do you draw a horizontal line that passes through the y- axis and through the sketched functions? Likewise when you choose your y limits, do you draw a vertical line that passes through the x axis and through the sketched functions? Also just wondering whether the shaded area is only half of the region to integrate? Maybe I could only integrate that half area and double the answer?

#### Attachments

• integral sketch.JPG
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Astronuc
Staff Emeritus
Please try to improve sketches of problems.

I think the double integral is

$$\int^1_0\,\int^1_{\sqrt{x}}\,\sqrt{1+y^3}\,dy dx$$

Ok,

draw a straight line parallel to y-axis that goes through your currently shaded region.

now, they are saying that y limits from going from sqrt(x) to 1

so, pick the starting point on the vertical line and the ending point.\

Astronuc, yea that is the right integral. But now, i dont know whether my shaded region is the right one?

Oh and rootX, dont u find out the limits after you know which area to integrate under?

Oh and rootX, dont u find out the limits after you know which area to integrate under?

Limits are given. Those dy goes from sqrt(x) to 1 and dx from 0 to 1

HallsofIvy