If ^4 x x^2-1 d x= (k)^ , then is equal to

Step-by-step solution

₁^4 x x^2-1 d x= (k)^ Let I= ₁^4 x x^2-1 d x Let x^2-1=t x d x= d t 2 Upper limit =t=4^2-1=15 Lower limit =t=1^2-1=0 aligned I & = ₀¹⁵ t d t 2 I & = 1 2 2 3 [t^ 3 / 2 ]₀¹⁵ I & = 1 3 [(15)^ 3 / 2 ]= k^ & = 1 3 , k=15 and = 3 2 & = 1 3 3 2 = 1 2 aligned