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Have we learned how to find antiderivatives with products? This is in reference to question 1b.
ReplyDeleteDahvi Lupovitch
Not yet, but soon! It will require a technique called Integration By Parts (IBP).
DeleteOn the SP p.312 #21, how do you take the integral of cos^2x?
ReplyDeleteUse the power reducing identity for cos^2.
DeleteReplace it with the hint they give you and then take the integral of that instead
DeleteI have a general question involving definite/indefinite integrals- Problems involving sin and cos and the U sub method are kind of difficult because there are so many different identities and properties that could apply. Is there a way to know which property to use quickly or is it more of a guess and check and think through type of thing? Also, do we have to memorize all of the properties and identities on our green sheets? (Sam Zerafa)
ReplyDeleteU sub is helpful for taking an anti derivative from a chain rule, i.e. A composition of two functions. Always look to use u sub on the inner most function. Sometimes it's necessary to use trig identities to get a function into a form where the integral is easier to find. It is a bit of trial and error and a bit more of being able to recognize derivatives. You should know your green sheets thoroughly, especially the double angle identities for sin and cos.
DeleteOn pg. 321 #5, it gives you u=(x/3) but why isnt u=(x^2)+9?
ReplyDeleteBecause there is no X term in Th numerator, letting u=x^2 will not allow du to cancel. By letting u=X/3, we are able to get a recognizable derivative of arctan. Handy trick.
DeleteFor 7c why does the variable change from n to x? Is there a specific reason or just mistyped?
ReplyDelete^Michael Pastoria
DeleteI do not have a copy in front of me. I will check tomorrow.
DeleteFor 4a In order to find the u how could you split the x^5 into seperate parts to make the equation work or is there a different method to do this that we have not learned yet
ReplyDeleteThis cannot be done with U sub.
DeleteHow do we find the antiderivative to solve 4a? Is there a trick I'm missing or am I approaching the question the wrong way?
ReplyDeleteDahvi Lupovitch
If f is the anti derivative of (x^2/1+x^5) then that means f=the integral of the function, and because you know what f(1) is and you can use your calculator, you can solve for f(4)
DeleteFor 1b it says find "an" antiderivative. If I put +c is that acceptable even though it encompasses all antiderivatives? Or should I just add a random constant
ReplyDeleteAdding C to the end is acceptable for this question.
DeleteCan C=0?
DeleteFor 6D, can tabular integration be used in order to find the position of the apricot?
ReplyDeleteYes, you can use tabular integration with the equation tcost.
DeleteActually thought Michaela wrote "equation toast" for a minute...now I'm hungry :)
DeleteFor 7b I was thinking to take the second derivative of T and find where that equals zero to find the point of inflections for T so that I can find where T is concave up, but I can't figure out how to factor that out and solve for n without using a calculator... Is there another approach I should be taking to solve this?
ReplyDelete- Evan Gilman
You should be able to factor out an exponential GCF, leaving you with a quadratic function.
DeleteOn problem 3, does the capital letters in R(t) and D(t) imply anti derivatives?
ReplyDeleteNo, those are the given RATE functions. This problem is very similar to the final exam question we discussed in class.
DeleteDoes anyone know if the double substitution is required to solve 5?
ReplyDeleteUse the formula for IBP here.
DeleteFor 1c on the turn in, I set the equation to 0 but I'm not sure where to go from there?
ReplyDeleteUse the antiderivative expression you found in part b to evaluate the definite integral (one of the limits being the unknown you wish to solve for). Let your calculator do the heavy lifting from there. No more hints from me tonight... :)
DeleteFor 5a are we allowed to use product rule for something that's inside a sum?
ReplyDeleteon #5 of the homework, can we still use the finger rule if the nominator is a polynomial?
ReplyDeleteEstelle
Yes, you just have to solve the top as well with the number that would make the denominator zero.
DeleteOn the "Techniques of Integration #2" worksheet, I can't seem to figure out how to do #8. I don't know what to use for u.
ReplyDeleteI don't have a copy at home with me. Can you post the question, please?
Delete