Question

Help with substitution method. Medals!!

Answer 1

what is it

Answer 2

good question

Answer 3

try u = pi/x^2

Answer 4

got that and then du= (-2pi/(x^3))dx

Answer 5

looks good

Answer 6

then do i integrate a=1 and b=3pi

Answer 7

into u and du?

Answer 8

oh hey sourwing

Answer 9

do the indefinite integral first,
then plugin the given point to find the constant C maybe...

Answer 10

ok got it

Answer 11

so it's now (pi/-x)*(2pi/-2x^2)

Answer 12

or is it ((pi-pix)/x^2)+C

Answer 13

\(\large \dfrac{dy}{dx} = \dfrac{\cos(\pi/x^2)}{x^3}\)

\(\large \implies\)

\(\large y = \int \dfrac{\cos(\pi/x^2)}{x^3}dx\)

sub \(u = \pi/x^2 \implies du = -2\pi/x^3 dx \implies \dfrac{1}{x^3}dx = \dfrac{-du}
{2\pi}\)

the integral becomes :

\(\large y = \int \cos(u) \frac{-du}{2\pi}\)


\(\large y = \frac{-1}{2\pi}\int \cos(u)du\)

Answer 14

evaluate..

Answer 15

(-sin(pi/x^2)/2pi)+C

Answer 16

yes !

\(\large y = -\dfrac{\sin (\pi/x^2)}{2\pi} + C\)

Answer 17

plugin the given point, and find out the constant \(C\)

Answer 18

k now plug n chug, i got it from here. thanks