Both of your answers are correct! Good job.

[Saladsamurai]

Definite Integrals

I think I got these, but I left my text at work, so I was hoping someone could confirm that these answers are correct?

a.)
$$\int_{-1}^{1}\frac{dx}{1+x^2}$$
$$=\tan^{-1}(1)-\tan^{-1}(-1) =-\frac{\pi}{2}$$

and

b.)
$$\int_0^{\ln5}e^x(3-4e^x)$$
$$=\int_0^{\ln5}[3e^x-4e^{2x}]dx$$
$$=3e^x-2e^{2x}]_0^{\ln5}=49$$

Thanks,
Casey

 

[Dick]

No on both. You have a horrendous sign error on the first. On the second, it's just plain all wrong, even though the integration is correct. What gives?

 

[Saladsamurai]

No on both. You have a horrendous sign error on the first. On the second, it's just plain all wrong, even though the integration is correct. What gives?

No sleep.

The first one I am al effed up on...I thought arctan(1)=pi/4 and arctan(-1)=3pi/4 ?? my calculator is saying it is +pi/2 What does give?

part 2...if the integration is correct, I don't know maybe I am putting it in the calculator wrong...maybe I should not need a calculator for this..but I suck at powers of e...even though I know they are supposed to be easy.

 

[Saladsamurai]

3e^{ln5)=15...4e^{2ln5} is where I think I am messing it up...
I do not remember how to evaluate...

...4*ln25=100?

 

[Saladsamurai]

$$\int_0^{\ln5}e^x(3-4e^x)$$
$$=\int_0^{\ln5}[3e^x-4e^{2x}]dx$$
$$=3e^x-2e^{2x}]_0^{\ln5}=86$$Maybe?

 

[Dick]

arctan(-1)=-pi/4. exp(2*ln(5))=5^2=25. Etc, etc. I think you need to get some sleep.

 

[Saladsamurai]

arctan(-1)=-pi/4. exp(2*ln(5))=5^2=25. Etc, etc. I think you need to get some sleep.

Getting up at 3:30 am for work is not all it's cracked up to be. You are right though...my 24 hour streak is about over. In the AM I will need to look over that e to the ln crap.

Thanks

 

[Saladsamurai]

$$\int_0^{\ln5}e^x(3-4e^x)$$
$$=\int_0^{\ln5}[3e^x-4e^{2x}]dx$$
$$=3e^x-2e^{2x}]_0^{\ln5}=36$$
...Can someone tell me if this is correct, or if I should just kill myself now :/

Casey

 

[Gib Z]

Closer, its actually -36. Get some sleep man, I remember once I stayed awake 30 hours, I walked home laughing at nothing...not a pretty sight for people walking by I'd imagine. Your not too far off insanity mate.