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?
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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:
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