Question

how to integrate sin(t^3)dt?

Answer 1

probably not possible

Answer 2

i mean to find a closed form

Answer 3

how so?

Answer 4

just because you write down some function does not mean you can find another function in closed form whose derivative is that thing

Answer 5

its a multiple choice question and no solution is not an option though

Answer 6

you can always write
\[\int_a^x\sin(t^3)dt\] as an anti - derivative, but you probably cannot find some function as an equation whose derivative you have

Answer 7

what does the question say exactly?

Answer 8

\[\int\limits_{x ^{2}}^{0} \sin(t ^{3}) dt\]sin(t^3)dt

Answer 9

x2 will be at the top though and 0 will be at the bottom

Answer 10

hold the phone. does it ask for the derivative???

Answer 11

no just integrate

Answer 12

find the derivative of
\[\int_0^{x^3}\sin(t^3)dt\]? maybe?

Answer 13

yes actually you are right
im sorry

Answer 14

how'd i guess?

Answer 15

how would i solve that?

Answer 16

the derivative of
\[\int_0^{x^2}\sin(t^3)dt\] requires the chain rule .
the derivative of the integral is the integrand, but you have a composite function because the upper limit of integration is x^2 not x

Answer 17

so replace t by x^2 and then multiply by the derivative of x^2 which is 2x

Answer 18

you will get
\[\sin((x^2)^3)\times 2x=2x\sin(x^6)\]

Answer 19

problem is actually very easy if you know what it is asking. the derivative of
\[\int_a^xf(t)dt\] is
\[f(x)\]

Answer 20

but in your case you have a composition, it is not
\[\int_a^xf(t)dt\] but rather
\[\int_a^{x^2}f(t)dt\] so by the chain rule you replace t by x^2 and then multiply by the derivative

Answer 21

for this i give myself the carnak award

Answer 22

Just make a wild guess:
Direvative of integral cancel out, then replace the limit = - sinx^6