Question

here is a fun one:
if \[x\sin \pi x=\int_{0}^{x^2}f(t)dt\], where f is continuous
find f(4)

Answer 1

hmmm very funny question
seem like fun fun!!!!!!!!!!!!!1

Answer 2

isn't it fun ? @Nnesha haha

Answer 3

@freckles would like this one but offline now darn ^^

Answer 4

nope i don't think so

Answer 5

Not an Infinite Series

Answer 6

Not an Infinite Series

Answer 7

okay let me see my attempt:
\[\frac{d}{dx}(x\sin \pi x)=\frac{d}{dx}\int_{0}^{x^2}f(t)dt\]
\[\sin \pi x+\pi x\cos \pi x=2xf(x^2)\]
\[f(x^2)=\frac{\sin \pi x+\pi x\cos \pi x}{2x}\]
\[f(2^2)=\frac{\sin2\pi +2\pi \cos 2\pi}{4}\]
\[f(4)=\frac{2\pi}{4}=\frac{\pi}{2}\] \[\square\]

Answer 8

@Nnesha see quite fun one :)

Answer 9

@perl check if this is correct

Answer 10

yes i agree

Answer 11

nice work :)

Answer 12

thanks :)

Answer 13

this was in problem plus section LOL i'm falling in love with it heheh