Question
Find the area of the region bounded by the following curves
5.
and the
-axis on
5.
Ask by Cervantes Horton. in the United States
Jan 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The area of the region bounded by
,
, and the
-axis on
is
.
Solution

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Bonus Knowledge
To find the area of the region bounded by the curves
,
, and the
-axis on the interval
, we need to first identify the points of intersection of
and
. They intersect when
, which occurs at
.
Next, we determine which function lies above the other in the interval
and
:
- In
, is greater than (for instance, at and ). - In
, is greater than (at and ).
Now we compute the area:
Calculating the first integral:
Calculating the second integral:
Adding both results gives us the total area:
Thus, the area of the region bounded by the curves is: