If 1 ^3 x x d x= k x +c then the value of k is

Step-by-step solution

Let I = 1 ³ x x dx . Rewrite the integrand as I = 1 ² x x x dx = 1 x x x dx . Divide the numerator and denominator by ² x inside the square root or manipulate the expression as follows: I = 1 x x x ² x dx = 1 x x x dx . Multiply numerator and denominator by ² x : I = ² x x x dx = ² x ( x)^ 3/2 dx . Substitute u = x , then du = ² x dx . I = u^ -3/2 du = u^ -1/2 -1/2 + c = -2 u^ -1/2 + c = -2 1 x + c . Comparing this with the given form k x + c , we find k = -2 . Answer: -2