Question

Let R be the region in the first quadrant bounded by the x-axis, the graph of x=y2+2, and the line x=4. What is a the interval for the area of R?

Answer 1

Answer:

x

goes from  

2

to  

4

and  

y

goes from  

0

to  

√

2

.

Explanation:

Sketch the graph of  

x

=

y

2

+

2

by sketching the sideways parabola  

x

=

y

2

then adding  

2

to the  

x

coordinates (translate  

2

to the right).

Add the  

x

axis and the vertical line  

x

=

4

to the picture:

enter image source here

The area can be found by either

∫

4

2

√

x

−

2

/

d

x

or by

∫

√

2

0

(

4

−

(

y

2

+

2

)

)

/

d

x

Step-by-step explanation: