[College - Calculus 1] Definite Integrals & Substitution

**rushyrulz** · 12-1-2010, 09:27 PM

halp!

Thanks

I already know the answer, I just don't quite get the process.

**rushyrulz** · 12-1-2010, 09:43 PM

bump. Calling all Rubix!

**smartdude1212** · 12-1-2010, 09:47 PM

Gah, I start learning this stuff in a month. You couldn't have waited? :P

I'm still trying to manipulate everything though based on what I know but I haven't come up with anything yet.

**rushyrulz** · 12-1-2010, 09:50 PM

I think the d/dx and the integral cancel, leaving e^(x^2)

then I plugged in the upper bound minus the lower bound and got:
(e^cos^2(x))-e

not sure if this is right tho.

**iironiic** · 12-1-2010, 09:55 PM

Fundamental Theorem of Calculus states that the answer is e^(cos^2(x)) (-sin(x))

Here's the wiki if you need to reference to it:
http://en.wikipedia.org/wiki/Fundame...em_of_calculus

EDIT: Oh oops, you need to use Chain Rule too. Forgot cos(x) is a function of x lol.

Wineandbread · 12-1-2010, 09:57 PM

iirc substitute cos(x) in place of t, change dt into dx, and append the derivative of cos(x) onto the back

derivative and the integral "cancel out", as you might say, and you're left with [e^(cosx)^2]*(-sinx)

Wineandbread · 12-1-2010, 09:57 PM

iirc substitute cos(x) in place of t, change dt into dx, and append the derivative of cos(x) onto the back

derivative and the integral "cancel out", as you might say, and you're left with [e^(cosx)^2]*(-sinx)

**Jtehanonymous** · 12-1-2010, 10:03 PM

Ooooh, so this is why you asked me if I was busy on aim.

You should've just said you needed help with a quick Calc problem. XD

**smartdude1212** · 12-1-2010, 10:08 PM

Wineandbread, you differentiated e^cos^2x improperly--it should be -2sinxcosx*e^cos^2x (aka -sin2x*e^cos^2x)

I think... XD

**rushyrulz** · 12-1-2010, 10:15 PM

Wineandbread is right.

The answer is (-e^cosx^2)*(sinx)

EDIT: This teacher is evil... I just solved an area problem using the Mean Value Thm. for Integrals and the answer was 1.553. And yes, it's the correct answer, I checked.

Who the hell writes a problem with that weird of an answer? I was surprised I got it right.

**smartdude1212** · 12-1-2010, 10:18 PM

Okay **** me I better run off and shoot myself before I spread the disease.

**rushyrulz** · 12-1-2010, 10:24 PM

Okay someone tell me what I'm doing wrong on this one:

I'm guessing I need to evaluate the antiderivative at F(b)-F(a)

When I integrate 4sec^2(x)-pi/x^2 I get: 4tanx-pi/x.

Is it just me or is tan(-pi/2) divide by 0?

I'm not getting a solution here.. if there even is one.

Wineandbread · 12-1-2010, 10:24 PM

you take the derivative with respect to the boundary, not the (cosx)^2

Hope your calc class takes a turn for the better rushy

My 3D calc class is killing me all over the place right now

tangomango · 12-1-2010, 10:48 PM

Wineandbread, are you taking multivariable? I'm probably going to take that next year...

**Jtehanonymous** · 12-1-2010, 10:51 PM

Quote:

Originally Posted by Wineandbread

My 3D calc class is killing me all over the place right now

I'm studying for my 3D calc final exam right now. It's in a week.

**travman301** · 12-1-2010, 10:55 PM

Are you a math major or something Jteh?

**smartdude1212** · 12-1-2010, 10:55 PM

Well the function isn't continuous on the interval, rushy, so you can't evaluate it using the FTC.

cos^2x =/= 0, x =/= +/- (2n+1)pi/2, etc.

**rushyrulz** · 12-1-2010, 10:57 PM

Okay thanks guys, I'll just stick with No Solution on that one. Done with the assignment

**Jtehanonymous** · 12-1-2010, 10:58 PM

Quote:

Originally Posted by travman301

Are you a math major or something Jteh?

Yup. =)

Rushy: Yay!

**smartdude1212** · 12-1-2010, 10:59 PM

Unless you want to start discussing complex infinity.

12-1-2010, 09:27 PM	#1
rushyrulz Digital Dancing! Join Date: Feb 2006 Location: 80 billion club, NE Age: 31 Posts: 12,980	[College - Calculus 1] Definite Integrals & Substitution halp! Thanks I already know the answer, I just don't quite get the process. __________________

12-1-2010, 09:43 PM	#2
rushyrulz Digital Dancing! Join Date: Feb 2006 Location: 80 billion club, NE Age: 31 Posts: 12,980	Re: [College - Calculus 1] Definite Integrals & Substitution bump. Calling all Rubix! __________________

12-1-2010, 09:47 PM	#3
smartdude1212 2 is poo Join Date: Sep 2005 Age: 32 Posts: 6,687	Re: [College - Calculus 1] Definite Integrals & Substitution Gah, I start learning this stuff in a month. You couldn't have waited? :P I'm still trying to manipulate everything though based on what I know but I haven't come up with anything yet.

12-1-2010, 09:50 PM	#4
rushyrulz Digital Dancing! Join Date: Feb 2006 Location: 80 billion club, NE Age: 31 Posts: 12,980	Re: [College - Calculus 1] Definite Integrals & Substitution I think the d/dx and the integral cancel, leaving e^(x^2) then I plugged in the upper bound minus the lower bound and got: (e^cos^2(x))-e not sure if this is right tho. __________________

12-1-2010, 09:55 PM	#5
iironiic D6 FFR Legacy Player Join Date: Jan 2009 Age: 32 Posts: 4,342	Re: [College - Calculus 1] Definite Integrals & Substitution Fundamental Theorem of Calculus states that the answer is e^(cos^2(x)) (-sin(x)) Here's the wiki if you need to reference to it: http://en.wikipedia.org/wiki/Fundame...em_of_calculus EDIT: Oh oops, you need to use Chain Rule too. Forgot cos(x) is a function of x lol. Last edited by iironiic; 12-1-2010 at 10:10 PM..

12-1-2010, 10:08 PM	#9
smartdude1212 2 is poo Join Date: Sep 2005 Age: 32 Posts: 6,687	Re: [College - Calculus 1] Definite Integrals & Substitution Wineandbread, you differentiated e^cos^2x improperly--it should be -2sinxcosxe^cos^2x (aka -sin2xe^cos^2x) I think... XD Last edited by smartdude1212; 12-1-2010 at 10:14 PM..

12-1-2010, 10:15 PM	#10
rushyrulz Digital Dancing! Join Date: Feb 2006 Location: 80 billion club, NE Age: 31 Posts: 12,980	Re: [College - Calculus 1] Definite Integrals & Substitution Wineandbread is right. The answer is (-e^cosx^2)(sinx) EDIT: This teacher is evil... I just solved an area problem using the Mean Value Thm. for Integrals and the answer was 1.553. And yes, it's the correct answer, I checked. Who the hell writes a problem with that weird of an answer? I was surprised I got it right. __________________ Last edited by rushyrulz; 12-1-2010 at 10:17 PM..*

12-1-2010, 10:18 PM	#11
smartdude1212 2 is poo Join Date: Sep 2005 Age: 32 Posts: 6,687	Re: [College - Calculus 1] Definite Integrals & Substitution Okay **** me I better run off and shoot myself before I spread the disease.

12-1-2010, 10:24 PM	#12
rushyrulz Digital Dancing! Join Date: Feb 2006 Location: 80 billion club, NE Age: 31 Posts: 12,980	Re: [College - Calculus 1] Definite Integrals & Substitution Okay someone tell me what I'm doing wrong on this one: I'm guessing I need to evaluate the antiderivative at F(b)-F(a) When I integrate 4sec^2(x)-pi/x^2 I get: 4tanx-pi/x. Is it just me or is tan(-pi/2) divide by 0? I'm not getting a solution here.. if there even is one. __________________

12-1-2010, 10:48 PM	#14
tangomango FFR Player Join Date: May 2007 Posts: 1,134	Re: [College - Calculus 1] Definite Integrals & Substitution Wineandbread, are you taking multivariable? I'm probably going to take that next year...

12-1-2010, 10:55 PM	#16
travman301 #swagdog Join Date: Mar 2004 Age: 33 Posts: 2,641	Re: [College - Calculus 1] Definite Integrals & Substitution Are you a math major or something Jteh?

12-1-2010, 10:57 PM	#18
rushyrulz Digital Dancing! Join Date: Feb 2006 Location: 80 billion club, NE Age: 31 Posts: 12,980	Re: [College - Calculus 1] Definite Integrals & Substitution Okay thanks guys, I'll just stick with No Solution on that one. Done with the assignment __________________

12-1-2010, 10:59 PM	#20
smartdude1212 2 is poo Join Date: Sep 2005 Age: 32 Posts: 6,687	Re: [College - Calculus 1] Definite Integrals & Substitution Unless you want to start discussing complex infinity. Last edited by smartdude1212; 12-1-2010 at 11:03 PM..

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