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

Question

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

mimi_x3 · Answer

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

mimi_x3 · Answer

Is that the integral?

mimi_x3 · Answer

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

anonymous · Answer

Yes limits given in questn

anonymous · Answer

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

lgbasallote · Answer

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

mimi_x3 · Answer

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

mimi_x3 · Answer

than me*

anonymous · Answer

I dont know how to do,pls giv me steps

anonymous · Answer

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