Starting with F(x)=∫(-2 to x) 3t^2(cos(t^3)+2)dt, use the substitution u(t)=t^3 to rewrite the definite integral.

Question

ganeshie8 · Answer

$\large  F(x) = \int \limits_{-2}^x  3t^2 (\cos(t^3) + 2)dt$

ganeshie8 · Answer

substitute $\large  u = t^3$

ganeshie8 · Answer

$\large  du = 3t^2  dt$

ganeshie8 · Answer

next work the bounds, 
do u knw how to figure out the new bounds for $u$ ?

anonymous · Answer

thank you for replying! I'm not completely sure, can you please help?

ganeshie8 · Answer

the original bounds are (-2, x) right ?

ganeshie8 · Answer

when u substitute u = t^3, 
the bounds change to  :

((-2)^3, x^3)

(-8, x^3)

ganeshie8 · Answer

so the integral becomes :-

$\large  F(x) = \int \limits_{-8}^{x^3}  (\cos(u) + 2)   du$

ganeshie8 · Answer

see if that makes some sense.. .

anonymous · Answer

aha! I didn't realize how simple that was. thank you!

ganeshie8 · Answer

:) u wlc !