Question

how do I integrate this?

Answer 1

\[\int\limits \frac{d^2 x}{dt^2} = \int\limits a\]

Answer 2

\[ \frac{d^2 x}{dt^2}=a \]
\[ \frac{d}{dt}(\frac{dx}{dt})=a \]
\[ \frac{d}{dt}(\frac{dx}{dt}) \ dt=a \ dt \]
\[\int \frac{d}{dt}(\frac{dx}{dt}) \ dt=\int a \ dt \]
\[ \frac{dx}{dt}= a \ t+C \]

Answer 3

another integration will give u x in terms of t

Answer 4

thank you! :D

Answer 5

yw :)

Answer 6

@mukushla if integral(f(x)) = integral(g(x)) ,, f(x) is not equal to g(x) -->please correct me if i am wrong
@lilMissMindset you need a "d" term (dx,da etc) on RHS with a to simplify
integral(a) doesnt make sense,,

Answer 7

sorry. i put the integration bar right away.

dt^2 will be transposing to the other side so that (a) can also be integrated.

Answer 8

@mukushla ohh sorry,,i take my words back
it was indefinite integral..and you diff both sides..hmm..sorry..

Answer 9

np :)

Answer 10

@lilMissMindset
u obtained it from a differential equation?

Answer 11

i think so.

Answer 12

i like your explanation. u explain better than my profs.

Answer 13

thats why i started with

\[ \frac{d^2x}{dt^2}=a \]

Answer 14

Oh...o.O... thank u.. :D

Answer 15

swear. :3

Answer 16

:)

Answer 17

how c came in last step may i know @mukushla

Answer 18

C is an arbitrary constant , thats constant of integration

Answer 19

oaky. thanks.
do it will come always in the last step of integration?

Answer 20

for indifinite integrals yes
The constant is a way of expressing that every function has an infinite number of different antiderivatives

Answer 21

you may treat whole question like motion of some particle :
d2x / dt2 = a
x = displacement
a= constant acceleration
which is easily understandable as dx/dt = velocity and dv/dt =a
now we have to find a relation between x,a and t, every other parameter might me taken C
which means 2nd eqn of motion:
x = ut + 1/2 a (t^2)
or
x= Ct + Kat^2

Answer 22

nice point

Answer 23

correction: you may not substitute K for 1/2