jmartinez638
  • jmartinez638
Calculate the following integrals:
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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jmartinez638
  • jmartinez638
\[A) \int\limits_{}^{}(y^2 + 4y - 7)dy\]
jmartinez638
  • jmartinez638
\[B) \int\limits_{}^{}\cos(2x)dx\]
jmartinez638
  • jmartinez638
\[C) \int\limits_{}^{}\sqrt{x^5}dx\]

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jmartinez638
  • jmartinez638
D) \[\int\limits_{0}^{\pi}x \sin tdt\]
anonymous
  • anonymous
A) \[\frac{ y ^{3} }{ 3 }+2y-7y+C\] where C represents a constant B) \[\frac{ 1 }{ 2 }\sin(2x)+C\] where C represents a constant C) \[\frac{ 2 }{ 7 }x ^{\frac{ 7 }{ 2 }}+C\] where C represents a constant D) I think you may have copied this wrong since there should only be one variable in the integrand for single integrals
jmartinez638
  • jmartinez638
Yeah, lemme see if I can find the original question(for D).
jmartinez638
  • jmartinez638
@Alphabet_sam It turns out that that equation is the "correct" one. Typo perhaps?
IrishBoy123
  • IrishBoy123
maybe D is the only interesting one, @Alphabet_Sam ?!?!?
IrishBoy123
  • IrishBoy123
for you!!
jmartinez638
  • jmartinez638
What do you think @IrishBoy123 ?
jmartinez638
  • jmartinez638
Also these here:
jmartinez638
  • jmartinez638
\[E) \int\limits_{0}^{x}cosx dx\]
jmartinez638
  • jmartinez638
F) \[F) \int\limits_{}^{}\frac{ x-3 }{ \sqrt{x} }dx\]
jmartinez638
  • jmartinez638
\[G) \int\limits_{3}^{0}7dt\]
jmartinez638
  • jmartinez638
\[H) \int\limits_{-4}^{4}(7t ^{51} - t) dt\]
jmartinez638
  • jmartinez638
@jim_thompson5910 I need some help understanding the process of calculating the integrals...
jim_thompson5910
  • jim_thompson5910
you need to post these one at a time @jmartinez638
jim_thompson5910
  • jim_thompson5910
which one is giving you the most trouble?
jmartinez638
  • jmartinez638
I apologize. Well since it's weird, D. H is also giving me a bit of trouble.
jim_thompson5910
  • jim_thompson5910
\[\Large \int_{0}^{\pi}x\sin(t)dt\] this?
jim_thompson5910
  • jim_thompson5910
I agree with @Alphabet_Sam it's very odd how there are 2 variables here. It suggest there is a typo somewhere
jim_thompson5910
  • jim_thompson5910
There's not much we can do really. You'll have to ask your teacher to clear up the problem. I have a feeling they'll say it's a typo too and give you the correct version. Did you want to move onto H now?
jmartinez638
  • jmartinez638
Sure!
IrishBoy123
  • IrishBoy123
\[\Large \int_{0}^{\pi}x\sin(t)dt\] \[\Large = x \int_{0}^{\pi}\sin(t)dt\]
jim_thompson5910
  • jim_thompson5910
x isn't usually a constant, but I guess you could treat it like one
jim_thompson5910
  • jim_thompson5910
Part H) \[\Large \int\limits_{-4}^{4}(7t ^{51} - t) dt\] \[\Large \int\limits_{-4}^{4}(7t ^{51})dt - \int\limits_{-4}^{4}(t) dt\] \[\Large 7\int\limits_{-4}^{4}(t ^{51})dt - \int\limits_{-4}^{4}(t) dt\] Do you see how to finish up?
jim_thompson5910
  • jim_thompson5910
You'll use this formula \[\Large \int(x^n)dx = \frac{x^{n+1}}{n+1}+C\]
jmartinez638
  • jmartinez638
\[7\int\limits_{-4}^{4}(t ^{51})dt - 0\]
jim_thompson5910
  • jim_thompson5910
idk how you got that `-0` part
jmartinez638
  • jmartinez638
If the first part of the integral minus the second part, the second parts is = 0
jmartinez638
  • jmartinez638
maybe i calculated something incorrectly...
jim_thompson5910
  • jim_thompson5910
the second part doesn't equal 0
jim_thompson5910
  • jim_thompson5910
oh nvm, I miscalculated
jim_thompson5910
  • jim_thompson5910
you're right \[\Large \int_{-a}^{a}f(t)dt = 0\] where f(t) is an odd function f(t) = t is an odd function
jim_thompson5910
  • jim_thompson5910
so is 7t^(51) since the exponent is odd
jmartinez638
  • jmartinez638
So the whole thing is = to zero
jim_thompson5910
  • jim_thompson5910
so in reality, you don't even have to find the integral since you can use this shortcut
jim_thompson5910
  • jim_thompson5910
yeah
jmartinez638
  • jmartinez638
That makes a lot of sense.
jmartinez638
  • jmartinez638
I'm going to work on these a little more in a bit. I will open another question if need be, but I doubt there will be any reason.

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