Question

F(x) = integrate t ^ 5 dt from 0 to x ^ 3 * then; = Box; f^ prime (x)=

Answer 1

Given the function f(x) as shown below.

`f(x)=\int_0^(x3)t^5dt`

Simplify the integral

`\int_0^(x3)t^5dt=\lbrack(t^(5+1))/(5+1)+C\rbrack_0^(x3)`
`\lbrack(t^(5+1))/(5+1)+C\rbrack_0^(x3)=\lbrack(t^6)/(6)+C\rbrack_0^(x3)`
`(((x^3)^6)/(6))-(0^6)/(6)`
`\therefore f(x)=(x^(18))/(6)`

Thus, the derivative of f(x) is:

`f^(\prime)(x)=(18* x^(18-1))/(6)=(18x^(17))/(6)=3x^(17)`

Final answer

`f^(\prime)(x)=3x^(17)`