Calling Calc'ers w/ beast skills

Test Preparation AP Test Preparation
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<p>Hi there. I need help w/ my calc homework [im in reg. calc, but i figured i could use the help of you AP Calc'ers or anyone else who is good at doing and explaining math ;D] I'm really bad at math, so please dont make fun of me.</p>

<p>Anyways, I've been doing all of these integration problems for finding volume using the disk method. for those of you who use the Calculus of a single variable book by Larson, Hostetler, and Edwards [Eighth Edition], thats the one I am using. Section 7.2</p>

<p>Ok. Could you please explain to me step by step what I am doing wrong? *i tried to use those internet, type in your equation, and we'll show you step by step things, but they were all trying to charge me money =S</p>

<p>so lets get to it! question 2- evaluate the integral that gives the volume of the solid formed by revolving the region about the x axis.</p>

<p>y = 4 - x^2 b/w areas of [0,2]
so volume = the integral of pi r ^2 . in this case, r is our function above</p>

<p>V= pi * integral [(4-x^2)^2, x, 0, 2]
so now we integrate...
V= pi * ((4-x^2)^3)/3 evaluate from 0 to 2</p>

<p>pi * (4- (2)^2)^3/3 - pi *(4 - 0^2) ^3)/3
= - 64/3 </p>

<p>apparently my answer is wrong [should be 256 pi/ 15 when i typed it in my calculator] but i don't know why!!!! HELP!</p>

<p>erm.. my other question [if it isnt too much of a burden. if it is, please just answer the first one, hopefully ill figure out what my blunder is]</p>

<h1>4</h1>

<p>y= the square root of: 9 - x^2</p>

<p>V= integral[pi*r^2 dx]
V= pi * the integral[9 -(x^2), x, 0, 3]
V= pi * [((9-(x^2))^2)/(2)] evaluate from o to 3</p>

<p>pi(9-3^2)^2/2 - pi* (9-0^2)^2/2
= -pi * 81/2 </p>

<p>but in my calculator, it says it should be eighteen pi!! please help, there is no point in doing anymore problems if i know im doing it wrong.</p>

<p>THANK YOU THANK YOU THANK YOU!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
bumble</p>

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<p>You can’t evaluate antiderivatives the way you’re doing it (this goes for both of the problems). So, for example, the antiderivative of (4-x^2)^2 would NOT be ((4-x^2)^3)/3. Try taking the derivative of that and you’ll see that you’ll get (4-x^2)^2 times -2x (since it isn’t the integral of, say, x(4-x^2)^2, you can’t use u-sub). To evaluate this integral by hand you have to multiply it out and then integrate, which isn’t as bad as it seems especially since you have 0 as one of your limits of integration and therefore do not need to take it into consideration when evaluating the integral using the fundamental theorem, but in other cases it can get messy, and for this you can almost always use the ti-89. On the AP Calc exams, they will only give you messy integrals on the free response and multiple choice with calculator; some of them might even be impossible to integrate by hand using normal methods (such as e^(x^2)). Otherwise, even though an integral might otherwise seem intimidating to evaluate by hand, if it says no calculator is allowed then you will see it should be very simple.</p>

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<p>oops… i can’t believe i didn’t think of opening it up.</p>

<p>thanks rhm 93!</p>