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