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anonymous
 one year ago
Need Help!
Evaluate the Definite integral with U substitution.
anonymous
 one year ago
Need Help! Evaluate the Definite integral with U substitution.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439090251436:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1look up the derivative of \(\sin^{1}x\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1substitute \(u=\sin^{1}x\) then \(du=?\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm confused on how you got U to be sin1x, how did you know it was that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I thought U was supposed what's inside roots or paretheses, such as 1x^2

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1do you know what the derivative of \(\sin^{1}x\) is ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yea...it's 1/srt 1x^2 * dx

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1that means substituting \(u = \sin^{1}x\) simplifies the integrand, because \(du = \dfrac{1}{\sqrt{1x^2}}dx\) that entire radical mess can be replaced by \(du\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So I can't always assume that whats inside the parentheses or roots is always going to be substituted as U, right?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1dw:1439090695448:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1No, with integrals there are no "strict" rules, you will have to do some guessing with each and every integral problem

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Also, don't forget to change the bounds accordingly

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1dw:1439090839359:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Why would I need to change the bounds?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1because with usubstitution you're changing the variable of integration, so the bounds also change accordingly

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1dw:1439090975245:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1those bounds refer to \(x\), they don't belong to \(u\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439091066367:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439091093678:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1no wait, whats the integrand right after substituting ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439091171917:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Yes, whats antiderivative of \(u\) with respective to \(u\) ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1nope, whats antiderivative of \(x\) with respect to \(x\) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh....so would it be U^2/2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but isnt U supposed to be thought of a constant, therefore it's antiderivative should be U of x?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\(u\) is not constant, it is the variable that has replaced \(\sin^{1}x\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439091490507:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So do I get a decimal answer when I evaluate the integral?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1plugin the bounds and see

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay so I got (sin1(1/2))^2/2? So do I box in that as the answer or its decimal...which is .137077

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1recall that \(\sin(\pi/6)=1/2\)

Ac3
 one year ago
Best ResponseYou've already chosen the best response.1look at the directions in the question

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The directions in the questions just say evaluate the integral.

Ac3
 one year ago
Best ResponseYou've already chosen the best response.1if it asks for EXACT answers which most professors want then you give them that

Ac3
 one year ago
Best ResponseYou've already chosen the best response.1never do decimal unless it specifically tells you to. We know that arcsin of 1/2 is pi/6 because of the unit circle

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ganeshie, is the answer (pi/6)^2/2?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lol i need help then..

Ac3
 one year ago
Best ResponseYou've already chosen the best response.1the answer i gave is wrong it should be pi/72 i'll show simplification right now one sec.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1nope thats still wrong

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes thats what I got too saseal!

Ac3
 one year ago
Best ResponseYou've already chosen the best response.1i meant to say pi^2/72 originally

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1yes leave it as \(\dfrac{\pi^2}{72}\) do not convert to decimals unless asked to do so

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, cool, thanks ganeshie!

Ac3
 one year ago
Best ResponseYou've already chosen the best response.1Usually with usubstitution the rule of thumb is to try and get something to go away with your Du. That's where knowing you derivatives really well comes in to play. When in doubt just guess and check.
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