Apr 30, 2013 Thread starter #1 A akbarali New member Apr 29, 2013 19 Last one for the night! These are the questions: This is my work: I think question 5 is correct (I hope), but I'm not entirely sure about question 6. Any help would be appreciated!
Last one for the night! These are the questions: This is my work: I think question 5 is correct (I hope), but I'm not entirely sure about question 6. Any help would be appreciated!
Apr 30, 2013 Admin #2 M MarkFL Administrator Staff member Feb 24, 2012 13,775 For the first one, I agree with your result. Good work! For the second one, the derivative form of the FTOC gives us: If: \(\displaystyle G(x)=\int_a^x f(t)\,dt\) then: \(\displaystyle G'(x)=f(x)\) You have cited a more general case, but can you see that you have added something to your result which should not be there?
For the first one, I agree with your result. Good work! For the second one, the derivative form of the FTOC gives us: If: \(\displaystyle G(x)=\int_a^x f(t)\,dt\) then: \(\displaystyle G'(x)=f(x)\) You have cited a more general case, but can you see that you have added something to your result which should not be there?
Apr 30, 2013 Thread starter #3 A akbarali New member Apr 29, 2013 19 Hmm, are you saying the answer should just be exp(sin(x)+ x^x) ?
Apr 30, 2013 Admin #4 M MarkFL Administrator Staff member Feb 24, 2012 13,775 Yes, your formula doesn't have $h'(x)$ in it, right?
Apr 30, 2013 Thread starter #5 A akbarali New member Apr 29, 2013 19 Is there any way you would work these problems differently from how I did that would help me better solve such problems in the future?
Is there any way you would work these problems differently from how I did that would help me better solve such problems in the future?
Apr 30, 2013 Admin #6 M MarkFL Administrator Staff member Feb 24, 2012 13,775 The first problem I would write: \(\displaystyle \int_0^{\pi}\sin(x)\,dx=-\left[\cos(x) \right]_0^{\pi}=-\left(\cos(\pi)-\cos(0) \right)=-(-1-1)=-(-2)=2\) For the second problem, I would simply write: \(\displaystyle \frac{d}{dx}\left(\int_0^x e^{\sin(s)+s^s}\,ds \right)=e^{\sin(x)+x^x}\)
The first problem I would write: \(\displaystyle \int_0^{\pi}\sin(x)\,dx=-\left[\cos(x) \right]_0^{\pi}=-\left(\cos(\pi)-\cos(0) \right)=-(-1-1)=-(-2)=2\) For the second problem, I would simply write: \(\displaystyle \frac{d}{dx}\left(\int_0^x e^{\sin(s)+s^s}\,ds \right)=e^{\sin(x)+x^x}\)
Apr 30, 2013 Thread starter #7 A akbarali New member Apr 29, 2013 19 You have been helping me all night. So grateful for your work. I have two more problems that are bugging the heck out of me, but I think I should let you rest for the night! Hehe
You have been helping me all night. So grateful for your work. I have two more problems that are bugging the heck out of me, but I think I should let you rest for the night! Hehe