Evaluate the integral by integration. Round your answer to two decimal places.
A) 4.00
B) 9.79
C) 0.71
D) 7.34
E) 3.77

Question

Evaluate the integral  by integration. Round your answer to two decimal places. ​
A) 4.00 
B) 9.79 
C) 0.71 
D) 7.34 
E) 3.77

Quizplus · Accepted Answer

To evaluate the integral, we need to perform integration by substitution. Let's take u = 4x - 4, which gives us du/dx = 4, or du = 4 dx. Plugging this into the integral, we get:

∫(4x-4) / sqrt(x-2) dx = ∫(1/4) * u / sqrt(u) du
= (1/4) * ∫sqrt(u) du
= (1/4) * [(2/3) * u^(3/2)] + C
= (1/6) * (4x-4)^(3/2) + C

Now we need to find the definite integral between 3 and 4. Plugging these in, we get:

(1/6) * [(4*4-4)^(3/2) - (4*3-4)^(3/2)]
= (1/6) * [(12^(3/2)) - (8^(3/2))]
= 9.79 (rounded to two decimal places)

Therefore, the answer is B.

Evaluate the Integral by Integration