Determine whether the improper integral diverges or converges. Evaluate the

tripiverded9

tripiverded9

Answered question

2022-01-07

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.
0161x4dx

Answer & Explanation

psor32

psor32

Beginner2022-01-08Added 33 answers

Step 1
Given:
0161x4dx...(1)
We know that : x4=(x)14
So, expression (1) becomes
=0161(x)14dx
=016(x)14dx
Step 2
=016(x)14dx
=[(x)14+114+1]016 (use xndx=xn+1n+1)
=[(x)3434]016
=[43(x)34]016
=43((16)340)
=43(8)
=323
if the limit is finite we say the integral converges,
So, The integral converge to 323

Durst37

Durst37

Beginner2022-01-09Added 37 answers

0161x4dx=limt0+t161x4dx
=limt0+t16x14dx
=limt0+(114+1x14+1)t16
=limt0+43x34t16
=limt0+(43(16)3443(t)34)
limt0+(43(t)34)=0
=43(16)340
=323

karton

karton

Expert2022-01-11Added 613 answers

Given:0161x4dxlima0+(a161x4dx)lima0+(324a343)Answer:323

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?