Question

How is the integral of (2-2t)dt, equal to 2t-2^2
Thanks!

Answer 1

using
\(\huge \int t^n dt =\dfrac{t^{n+1}}{n+1}+c\)

Answer 2

for 1st term , n=0 (2=2*t^0)
for 2nd term., n=1

Answer 3

bdw its 2t-t^2+c

Answer 4

I have no idea whats going on, shouldn't this be a simple integral?

Answer 5

it is.
use of just 1 formula.

Answer 6

using that formula, what will be integral of t dt ?

Answer 7

Yea I know its the tried and true integral formula I must have done 100 of them, and I can't do this right now, my wires must be crossed.

Answer 8

like the integral of x^2 is 1/3 x^3

Answer 9

integral of t dt is 1/2 t^2

Answer 10

yes, yes!
correct.

Answer 11

in same way, integral of 2 is 2t

Answer 12

I guess I don't get that part

Answer 13

like how do I just add the t in there

Answer 14

I get that the derivative of 2t is 2

Answer 15

not just adding 't'
using the formula
2 = 2t^0
so, exponent = n= 0
after integration
the exponent = n+1 = 0+1 =1
got this ?

Answer 16

yes I do thank you so much because you probably just saved me an ulcer

Answer 17

2 as a constant can be taken out of integral
thats why 2t

Answer 18

thats what I don't get

Answer 19

if the 2 comes out, doesn't it remain a 2

Answer 20

I'm thinking in derivative terms I guess where constants are dropped.
with integral it goes out front so it never gets integrated?

Answer 21

I guess its connected via subtraction to the 2t so it can't be pulled out

Answer 22

integral of any constant = constant * variable
integral of a dx = a* integral x^0 dx = ax+c

Answer 23

ok thanks for your help! Im gonna let this marinate.

Answer 24

welcome :)