SOLUTION: Consider the function {{{f(x) = sqrt(4-x^2)}}} Hint: This is the upper half of a circle of radius 2 positioned at (0, 0). Find the area (in {{{unit^2}}}) between the x-axis a

Question 1161227: Consider the function

Hint: This is the upper half of a circle of radius 2 positioned at (0, 0).
Find the area (in ) between the x-axis and the graph of f over the interval [−2, 2] using rectangles. For the rectangles, use squares 0.8 by 0.8 units, and approximate both above and below the lines.
above: ?
below: ?
Use geometry to find the exact answer (in ).
exact answer: ?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

I drew the half circle in red, and red and green 0.8unit by 0.8unit squares.
Each 0.8unit by 0.8unit square has an area of

The way I see, only the red 0.8 unit by 0.8 unit squares fit inside the half circle.
Their total area is the area approximated below the half circle .
The way I see, to completely cover the half circle, I need to use the red and green squares.
Those are squares.
Their total area is the area approximated above the half circle .
RELATED QUESTIONS
Consider f(x) = x^2 + 3, x < 0. What is the inverse of this... (answered by josgarithmetic)

Consider f(x) = x^2 + 3, x < 0. What is the inverse of this... (answered by Boreal,MathLover1)

Consider the circle x^2+y^2-6x-8y=0 Find the center and radius of the... (answered by ewatrrr)

consider this function: f(x)= x^3+ x^2- x + 1 What is the value of... (answered by algebrapro18)

Let the random variable X have the density function f(x)= {kx for... (answered by Greenfinch)

Consider the function f(x)=e^2*(x-1)^3. Draw a graph of the function on the interval... (answered by solver91311)

Find the center and radius of the circle... (answered by mathman409)

Find the center and radius of the circle... (answered by solver91311)

Consider f(x) = x2 + 3, x < 0. What is the inverse of this... (answered by josgarithmetic)