SOLUTION: Use the definite integral to find the area between the​ x-axis and​ f(x) over the indicated interval. Check first to see if the graph crosses the​ x-axis in the given interva

Algebra.Com
Question 1193558: Use the definite integral to find the area between the​ x-axis and​ f(x) over the indicated interval. Check first to see if the graph crosses the​ x-axis in the given interval.
​f(x)=16-x^2​; ​[0​,8​]
The area between the​ x-axis and​ f(x) is___
Please answer the area between the​ x-axis and​ f(x)

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Same problem, different numbers.
===========================================
Use the definite integral to find the area between the​ x-axis and​ f(x) over the indicated interval. Check first to see if the graph crosses the​ x-axis in the given interval.
----
​f(x)=36-x^2​;​[​-1,​12]
\=======================
x^2 = 36 ---> x-intercepts at -6 and +6
-------------------
Int(36 - x^2) = g(x) = 36x - x^3/3 + C
Area from -1 to +6 = g(6) - g(-1)
Area = 216 - (-36 + 1/3) = 179 2/3 sq units
=================
Area from 6 to 12:
Area = g(12) - g(6) = 288 sq units ------> you can do the calculations.
-----
The area from 6 to 12 is below the x-axis, sometimes viewed as negative.
Subtracting would give a negative area, so add them.

RELATED QUESTIONS

Use the definite integral to find the area between the​ x-axis and​ f(x) over (answered by Fombitz)
I need help! Use the definite integral to find the area between the x-axis and f(x)... (answered by richard1234)
Use the definite integral to find the area between the​ x-axis and​ f(x) over the... (answered by Alan3354)
re. function f(x)=(x-2)(1-e^x) a) I have to find points where the function crosses the... (answered by Boreal)
please help Find the area bounded between a) f(x) = 1/x and g(x) = x^2 on the... (answered by ikleyn)
Find the area bounded by the x-axis and f(x)=x^4-5x^2+4 and also show the result by (answered by Alan3354)
Hello, Please help me to find the solution to the following: Compute the definite... (answered by rothauserc)
How could the definite integral be used to determine profit over a given period? (answered by addingup)
Use an iterated integral to find the area of the region bounded by the graphs of f(x)=... (answered by Fombitz)