Confused at the theory behind these kinds of problems.

AloetheFerret

I would like some help solving these because it is difficult to conceptualize what's even going on.

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Cervesa

(a) use substitution

let $u = \dfrac{t}{4} \implies dt = 4 \, du$

lower limit is $t= 0 \implies u = \dfrac{0}{4} = 0$ , upper limit is $t=16 \implies u = \dfrac{16}{4} = 4$

$\displaystyle \int_0^{16} g\left(\dfrac{t}{4}\right) \, dt = \int_0^4 g(u) \cdot 4 \, du = 4 \int_0^4 g(u) \, du = 4 \cdot 3 = 12$

try the same method for (b)

topsquark

AloetheFerret

Yeah, I can't figure out b. Little help?

Plato

MHF Helper
Yeah, I can't figure out b. Little help?
Are you really saying that you cannot follow the exact steps for the part a?
$$\displaystyle u=4-t$$ then $$\displaystyle du=?$$
If $$\displaystyle t=0,~u=?~~\&~~t=4,~u=?$$