Question

how to integrate sint^2)

Answer 1

is it sin(t^2) or sin^2(t)

Answer 2

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

Answer 3

okay so do you know the anti-derivative of sine?

Answer 4

-cos

Answer 5

correct

Answer 6

i'm just confused with the t^2 in the inside

Answer 7

well if you where doing the derivative of -cos(t^2) what would you get?

Answer 8

2tsin(t^2) ?

Answer 9

right, but as we see in the integral there isnt a 2t, so therefore we must divide by 2t so cancel this out. Does that make sense?

Answer 10

Have you done integration using substitution?

Answer 11

yes.

Answer 12

u should make a substitution. u = t^2

Answer 13

then change the dt to du and change the limits and u then should just have to integrate sin u

Answer 14

i origninally thought the antiderivative was
\[-\frac{ t^3 }{ 3 } \cos(t^2)\]

Answer 15

shall I show u my method?

Answer 16

sure.