Evaluate the definite integral. \int_{0}^{2}\frac{dx}{\sqrt{2x+5}}

foass77W

foass77W

Answered question

2021-11-06

Evaluate the definite integral.
02dx2x+5

Answer & Explanation

lobeflepnoumni

lobeflepnoumni

Skilled2021-11-07Added 99 answers

Step 1
The integral is 02dx2x+5
Let 2x+5=u.
Thus,
2dx=du
dx=12du
Determine the new limits.
For x = 0
u=2(0)+5
=0+5
=5
For x=2
u=2(2)+5
=4+5
=9
Thus, the new limits are from 5 to 9.
Step 2
Substitute u for (2x + 5) and 12du for dx in 02dx2x+5 and also replace the limits.
02dx2x+5=1259duu
=1259(u)12du
=12[(u)1212]59
=12(2)[(9)12(5)12]
=[3-2.24]
=0.76
Thus, the integral value is 0.76.

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