Solve the integral. \int_{0}^{4}\frac{e^{\sqrt{x}}}{\sqrt{x}}dx

pierdoodsu

pierdoodsu

Answered question

2022-01-06

Solve the integral.
04exxdx

Answer & Explanation

Navreaiw

Navreaiw

Beginner2022-01-07Added 34 answers

Step 1: To Find
We have to evaluate the integral
04exxdx
Step 2: Calculation
Since we have the integral
04exxdx
Let u=x12xdx=du
when x=0 then u=0
when x=4 then u=2
04exxdx=022eudu
=202eudu
=2[eu]02   exdx=ex+C
=2[e2e0]
04exxdx=2[e21]
eninsala06

eninsala06

Beginner2022-01-08Added 37 answers

To evaluate the integral
04exxdx
we make the substitution
|x=ux=u2dx=2udu|
When
x=1u=1
and when
x=4u=4=2
Therefore,
04exxdx=20euu2udu
=202eudu
=2eu02
=2(e21)
We conclude that
04exxdx=2(e21)
Result:
04exxdx=2(e21)
karton

karton

Expert2022-01-11Added 613 answers

04exxdxlima0+(14exxdx)Evaluate the integral.lima0+(2e22ea)Answer:2e22

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