U substitution with definite integral

[jtt]

Homework Statement

make a u- substitution and integrate from u(a) to u(b)

Homework Equations

∫[0,1] √(t^5+2t) (5t^4+2) dt

The Attempt at a Solution

u= t^5+2t du= 5t^4+2

u(1)=2 u(0)=0

∫[0,1] √(u) du

(2/3)(u)^3/2+c l[0,2]

(2/3)( 0^5+2(0))^3/2- (2/3)(2^5+2(2))^3/2
0+ 24^3/2

the textbook answer is 2√3 but I don't know where I messed up

 

[SammyS]

Homework Statement

make a u- substitution and integrate from u(a) to u(b)

Homework Equations

∫[0,1] √(t^5+2t) (5t^4+2) dt

The Attempt at a Solution

u= t^5+2t du= 5t^4+2

u(1)=2 u(0)=0

∫[0,1] √(u) du

(2/3)(u)^3/2+c l[0,2]

(2/3)( 0^5+2(0))^3/2- (2/3)(2^5+2(2))^3/2
0+ 24^3/2

the textbook answer is 2√3 but I don't know where I messed up

u(1)=(1)⁵ +2(1) = 3 not 2 .