Question

Find what value of c does ∫₆[infinity]c/x⁴ d x=1 ?

Answer 1

The value of c for which the integral from 6 to infinity of c/x⁴ dx equals 1 is c = 108.

Step-by-step explanation:

The question asks for the value of c for which the integral from 6 to infinity of c/x⁴ dx equals 1. To find this value, we will perform the integration and solve for c.

First, we integrate:

1. ∫(inf) c/x⁴ dx = c ∫(inf) x⁻⁴ dx
2. = c [-1/(3x³)]⁶(inf)
3. = c [0 - (-1/(3×6³))] = c/(3×6⁳)

Now, we set the result equal to 1 and solve for c:

c/(3×6⁳) = 1

c = 3×6⁳

Thus, c = 108 is the value for which the given integral equals 1.