Evaluate the integral: a/100 – a* ,3 -

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Evaluate the integral:
Jæ° V100 – x?dæ
+ C
Question Help: D Video 1 D Video 2
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Transcribed Image Text:Evaluate the integral: Jæ° V100 – x?dæ + C Question Help: D Video 1 D Video 2 Submit Question
Expert Solution
Step 1

We have to evaluate the integral x3100-x2dx.

We shall solve this by substitution method. 
Let 100-x2=t2-2x dx = 2t dtx dx= -t dt.


x3100-x2dx =x2.100-x2.x dx                          =-(100-t2).t.t dt                          =-(100t2-t4) dt                          =-100t33-t55 + C                          =-100(100-x2)323+(100-x2)525+C
where C is the constant of integration.

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