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what is the integration of the term : 4x^3 root(5-x^2) dx

what is the integration of the term : 4x^3 root(5-x^2) dx

Grade:12

1 Answers

Snehal Jadhav
54 Points
3 years ago
The given indefinite integral can be found by using subsitution method:
 
∫4x3(5 – x2)1/2dx
 
Subsitute 5 – x2 as t2     :
  
    5–x2 = t2
 
 −2xdx = 2tdt
 
  −x dx = t dt
 
∫4x3(5 – x2)1/2dx = ∫4(t2 − 5)t dt
 
∫(4t3 – 20t)dt
 
t4 – 10t2 + c
 
Resubsitute the value of 5 – x2 as t2  :
 
(5 – x2) 2 – 10(5 – x2) + c
 
The final Answer is:
 
x4 – 25 + c
 

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