If x φ(x)=∫ limits5x(3 t2-2 φ prime(t)) d t, x-2, and φ(0)=4, then φ(2) is

Question

If x φ(x)=∫ limits5x(3 t2-2 φ prime(t)) d t, x>-2, and φ(0)=4, then φ(2) is  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

x φ(x)=∫ limits5x 3 t2-2 φ prime(t) d t x φ(x)=x3-125-2[φ(x)-φ(5)] x φ(x)=x3-125-2 φ(x)-2 φ(5) φ(0)=4 ⇒ φ(5)=-(133/2) φ(x)=(x3+8/x+2) φ(2)=4

Q. If $x ϕ (x) = 5 \int x (3 t^{2} - 2 ϕ^{'} (t)) d t, x > - 2$ , and $ϕ (0) = 4$ , then $ϕ (2)$ is ___