# calc

find the area between the x-axis and the graph of the given function over the given interval:

y = sqrt(9-x^2) over [-3,3]

you need to do integration from -3 to 3.
First you find the anti-derivative

when you find the anti-derivative you plug in -3 to the anti-derivative and then plug in 3 and find the difference of : f(-3)-f(3). Hope this helps :)

but how to you find the antideriv?

Paste sqrt(9-x^2) into

http://integrals.wolfram.com/index.jsp

This is an arcsin derivative.

Substitute x = 3 sin(t). Then t goes from - pi/2 to pi/2.

sqrt[9 - x^2] = 3 sqrt[1 - sin^2(t)] =

3 |cos(t)|

and dx = 3 cos(t) dt

So, you have to integrate 9 cos^2(t) from t = -pi/2 to pi/2 (note that in the interval cos(t) is positive so you can remoce the absolute value signs).

Since we are integrating over an entire period of the cos^2 the integral would be the same if you replace cos^2 by sin^2. By replacing cos^2 by cos^2 + sin^2 you thus obtain twice the value of the integral but since sin^2 + cos^2 = 1 that's 9 pi. So, the integral is 9/2 pi.

1. 👍 0
2. 👎 0
3. 👁 309

## Similar Questions

1. ### Math

Find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis, and a tangent line to the graph of y = (x+1)^-2

asked by Javier on November 12, 2010
2. ### calculas

Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval. (Round your answers to four decimal

asked by Sam on May 7, 2016
3. ### Calculus Finals Review sheet!! Explanation needed

Here is a graph of the derivative y' of a continuous, differentiable function. For approximately what values of x between Ã¢Ë†â€™5 and 5 does the original function y have inflection points? Find limit as x approaches 3.5

asked by Prince@18 on December 17, 2016
4. ### Gr.11 - Rational functions graphing.

1. Identify a rational function whose graph is a horizontal line except for two holes. Graph the function. 2. Identify a rational function who graph lies entirely above the x-axis and has a single vertical asymptote. Graph the

asked by Mae on October 6, 2008
1. ### Calculus

Use two rectangles of equal width to estimate the area between the graph of f(x)=x+sin( πx) and the x-axis on the interval [4,8]. Evaluate the function at the mid-point of each rectangle to find each height. a) 20 b) 24 c) 26 d)

asked by Alice on January 23, 2019
2. ### Math

compare the parent function f(x)=x^2 to the quadractic function f(x)=-2x^2-6. the 6 in the function does which of the following? a.it makes the graph narrower than the parent function. b.it makes the graph wider than the parent

asked by Adriana on March 2, 2018
3. ### Algebra (math)

The graph represents function 1 and the equation represents function 2: A graph with numbers 0 to 4 on the x-axis and y-axis at increments of 1. A horizontal straight line is drawn joining the ordered pairs 0, 3 and 4, 3. Function

asked by Winchester on January 4, 2017
4. ### Calculus

Use the limit process to find the area of the region between the graph of the function and the x-axis over the indicated interval. Sketch the region. y=2x-x^(3), [1,3]

asked by Simon on April 26, 2013
1. ### Algebra I

Rectangle ABCD has vertices C and d on the x-axis and vertices A and B on part of the parabola y = 9 - x^2 that is above the x-axis. a.) Find the coordinates of A, B, C, and D in terms of x. b.) Determine the Area of the rectangle

asked by Kate on July 28, 2010
2. ### Math

The graph represents function 1 and the equation represents function 2: A graph with numbers 0 to 4 on the x-axis and y-axis at increments of 1. A horizontal straight line is drawn joining the ordered pairs 0, 3 and 4, 3. Function

asked by Marc-Anthony on January 11, 2016
3. ### algebra

3. write the function whose graph is the graph of y=sqrt of x, but is shifted to the left 3 units y=____ 4. write the function whose graph is the graph of y=|x|, but is shifted down 8 units y=___ 5. write the function whose graph

asked by sharday on May 24, 2013
4. ### Algebra

A sine function has the following key features: Period = 4 Amplitude = 4 Midline: y = 1 y-intercept: (0, 1) The function is not a reflection of its parent function over the x-axis. Use the Desmos graph tool to graph the function.

asked by Annie on January 29, 2020