Question

Fq(x) = integrate sqrt(4 + z ^ 6) dz from 0 to x ^ s * then

Answer 1

We are given the definite integral:

`q(x)=\int_0^(x^8)√(4+z^6)dz`

We need to find q'(x).

We can use the fundamental theorem of calculus to solve this. Given a function F(x):

`F(x)=\int_a^bf(x)dx`

Then:

`F^(\prime)(x)=f(x)`

Thus, we can find the antiderivative q'(x), using the fundamental theorem of calculus and the chain rule:

`(d)/(dx)(\int_0^(x^8)√(4+z^6)dz)=√(4+(x^8)^6)\cdot(d)/(dx)(x^8)=\sqrt{4+x^(48)}\cdot8x^7`

The answer is:

`q^(\prime)(x)=8x^7\sqrt{4+x^(48)}`