Cross Section Volume Calc Please Help!?

Question

The base of a certain solid is the area bounded above by the graph of y=f(x)=9 and below by the graph of y=g(x)=25x^2. Cross-sections perpendicular to the -axis are squares. (See picture above, click for a better view.) 
Use the area formula The inegral of A(x)dx from a to b to find the volume of the solid. 

Note: You can get full credit for this problem by just entering the final answer (to the last question) correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit. 
The lower limit of integration is  =   (-3/5)
The upper limit of integration is  =   (3/5)
The side  of the square cross-section is the following function of :  
=  ?
Thus the volume of the solid is  =  ?

ted s · Accepted Answer

the typed area function means the squares are perpendicular to the x axis , as well as the limits.

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int over [ - 3 / 5 , 3 / 5 ] of { [ 9 - 25 x² ] ² dx }

? · Answer

what's the section you assert? nicely you have a sq.. what's the top of this sq.??? You already advised me what it replaced into. you pronounced the top of the semi circle that's 0.5 the top of the squaee is sqrt(sixty 4-x^2) Multiplu via 2 to get the excellent fringe of sq.. So its 2sqrt(sixty 4-x^2) what's the section if a sq.? Its component squared isnt it? I gave you the top. in case you sqaure it it is going to yield 4(sixty 4-x^2) Thats the section. And the quantity? Your limits are from -8 to eight Of the indispensable of the section you in undemanding terms chanced on 4(sixty 4-x^2)dx its indispensable is the 4(64x -(a million/3)x^3) from -8 to eight Then doing the fund thrm of calculus. you may obtain 8(sixty 4*8 -(a million/3)*(8^3)) Which i'm particular u can obtain without my help. Simplify the above expression to get ur quantity.

Cross Section Volume Calc Please Help!?

2 Answers