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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
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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