Calculate the following integrals:

- jmartinez638

Calculate the following integrals:

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- jamiebookeater

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- jmartinez638

\[A) \int\limits_{}^{}(y^2 + 4y - 7)dy\]

- jmartinez638

\[B) \int\limits_{}^{}\cos(2x)dx\]

- jmartinez638

\[C) \int\limits_{}^{}\sqrt{x^5}dx\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- jmartinez638

D) \[\int\limits_{0}^{\pi}x \sin tdt\]

- 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

Yeah, lemme see if I can find the original question(for D).

- jmartinez638

@Alphabet_sam It turns out that that equation is the "correct" one. Typo perhaps?

- IrishBoy123

maybe D is the only interesting one, @Alphabet_Sam ?!?!?

- IrishBoy123

for you!!

- jmartinez638

What do you think @IrishBoy123 ?

- jmartinez638

Also these here:

- jmartinez638

\[E) \int\limits_{0}^{x}cosx dx\]

- jmartinez638

F) \[F) \int\limits_{}^{}\frac{ x-3 }{ \sqrt{x} }dx\]

- jmartinez638

\[G) \int\limits_{3}^{0}7dt\]

- jmartinez638

\[H) \int\limits_{-4}^{4}(7t ^{51} - t) dt\]

- jmartinez638

@jim_thompson5910 I need some help understanding the process of calculating the integrals...

- jim_thompson5910

you need to post these one at a time @jmartinez638

- jim_thompson5910

which one is giving you the most trouble?

- jmartinez638

I apologize. Well since it's weird, D. H is also giving me a bit of trouble.

- jim_thompson5910

\[\Large \int_{0}^{\pi}x\sin(t)dt\]
this?

- 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

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

Sure!

- IrishBoy123

\[\Large \int_{0}^{\pi}x\sin(t)dt\]
\[\Large = x \int_{0}^{\pi}\sin(t)dt\]

- jim_thompson5910

x isn't usually a constant, but I guess you could treat it like one

- 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

You'll use this formula
\[\Large \int(x^n)dx = \frac{x^{n+1}}{n+1}+C\]

- jmartinez638

\[7\int\limits_{-4}^{4}(t ^{51})dt - 0\]

- jim_thompson5910

idk how you got that `-0` part

- jmartinez638

If the first part of the integral minus the second part, the second parts is = 0

- jmartinez638

maybe i calculated something incorrectly...

- jim_thompson5910

the second part doesn't equal 0

- jim_thompson5910

oh nvm, I miscalculated

- 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

so is 7t^(51) since the exponent is odd

- jmartinez638

So the whole thing is = to zero

- jim_thompson5910

so in reality, you don't even have to find the integral since you can use this shortcut

- jim_thompson5910

yeah

- jmartinez638

That makes a lot of sense.

- 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.

Looking for something else?

Not the answer you are looking for? Search for more explanations.