If ∫x21-xdx=p1-x3x2+4x+8, then the value of p is:
-215
215
415
None of these
Explanation for the correct option:
Integration:
∫x21-xdx
Let 1-x=t2 then x=1-t2anddx=-2tdt. So,
∫x21-xdx=-2∫t1-t22tdt=-2∫1-2t2+t4dt=-2t-2t33+t55+c=-215t-10t3+3t515+c=-2t15-10t2+3t415+c
By substituting the value of t, we get
=-21-x15-101-x+31-x215+c=-21-x15-10+10x+3+3x2-6x15+c=-21-x153x2+4x+8
So, p=-215
Hence, option A is correct.