Question

Calculate the following integrals:

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

for you!!

Answer 10

What do you think @IrishBoy123 ?

Answer 11

Also these here:

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

you need to post these one at a time @jmartinez638

Answer 18

which one is giving you the most trouble?

Answer 19

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

Answer 20

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

this?

Answer 21

I agree with @Alphabet_Sam
it's very odd how there are 2 variables here. It suggest there is a typo somewhere

Answer 22

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?

Answer 23

Sure!

Answer 24

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

Answer 25

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

Answer 26

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?

Answer 27

You'll use this formula

\[\Large \int(x^n)dx = \frac{x^{n+1}}{n+1}+C\]

Answer 28

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

Answer 29

idk how you got that `-0` part

Answer 30

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

Answer 31

maybe i calculated something incorrectly...

Answer 32

the second part doesn't equal 0

Answer 33

oh nvm, I miscalculated

Answer 34

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

Answer 35

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

Answer 36

So the whole thing is = to zero

Answer 37

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

Answer 38

yeah

Answer 39

That makes a lot of sense.

Answer 40

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.