## sarathkothapalli 3 years ago Integral of (x^3.^root(4x-x^2) dx with integral limits 0,4 Integral of x^4/(1+x^2)^4 dx with integral limits 0,5 pls giv me solution for above 2 questns in detailled steps

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1. Mimi_x3

$\int x^{3}\sqrt{x^{2}-4} dx$

2. Mimi_x3

Is that the integral?

3. Mimi_x3

I mean: $\large \int\limits x^{3}\sqrt{4x-x^{2}} dx$?

4. sarathkothapalli

Yes limits given in questn

5. sarathkothapalli

Pls giv me slution in steps as i need to note it

6. lgbasallote

i think you're supposed to do completing the swuare here

7. Mimi_x3

well, it's completing the square first then trig-sub. Why not you try it; then me typing the solution for you?

8. Mimi_x3

than me*

9. sarathkothapalli

I dont know how to do,pls giv me steps

10. exraven

$4x - x^2 = -(x^2 - 4x)$$= -(x^2 - 4x) - 4 + 4$$= -(x^2 - 4x + 4) + 4$$= 4 - (x^2 - 4x + 4)$$= 4 - (x - 2)^2$$\int\limits x^3 \sqrt{4x - x^2}dx = \int\limits x^3 \sqrt{4 - (x - 2)^2} dx$there i already completed the square for you, just do trig subs and you'll be fine