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
himadri tripathi , 7 Years ago
Grade 12
Integral Calculus> what is the integration of the term : 4x^...
1 Answers
Snehal Jadhav
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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