I think the answer is -3x^2cos(x^12) but i am second geussing myself a lot some concrete explenation would go miles
https://gyazo.com/f14d2c1466886819d59f9a8ec2e1ecb0

Question

I think the answer is -3x^2cos(x^12) but i am second geussing myself a lot some concrete explenation would go miles
https://gyazo.com/f14d2c1466886819d59f9a8ec2e1ecb0

satellite73 · Answer

yes you are right

anonymous · Answer

WHEEEEW
that means im officially 100% done with my honours calc course

satellite73 · Answer

the reason it is minus is because first you can change it to $$-\int_1^{x^2}\cos(t^4)dt$$

scooby6363 · Answer

Congrats

anonymous · Answer

but lets hear that explenation

satellite73 · Answer

then use two facts: the derivative of the integral is the integrand, and the chain rule

satellite73 · Answer

i.e. replace $t$ by $x^3$ and also multiply by the derivative of $x^3$ which is $3x^2$

anonymous · Answer

Ok, yeah Thats what i figured but a cheased it at the replacing t part i just geussed that one

satellite73 · Answer

that is what you do !