How do you solve #int_0^1 sqrt(5x+4) dx#?

1 Answer
Jan 17, 2017

#38/15#

Explanation:

We need to use a u-substitution to solve this question.

STEP 1: Identify the u
#u = 5x+4#

STEP 2: Find du
#du = 5 dx#

STEP 3: Change the x-bounds to u-bounds
#x = 0 -> u = 5(0)+4 = 4#
#x = 1 -> u = 5(1)+4 = 9#

STEP 4: Do the u-substitution
#int_0^1 sqrt 5x+4 dx#
#=int_4^9 sqrt(u) * 1/5 du#
remember: we found #du = 5dx#, so if we solve for #dx# we get #dx=1/5 du#
#=1/5 int_4^9 sqrt(u) du#
#=1/5 [2/3 u^(3/2)]_4^9#
#=2/15[u^(3/2)]_4^9#
#=2/15(3^3 - 2^3)#
#=2/15(19)#
#=38/15#