Question

Find the general antiderivative of the function g(x)= oot(4)(x^(3))+ oot(3)(x^(4)) Supporting work must be provided.

Answer 1

(x^(3/4) + x^(4/3)) dx = (4/7)x^(7/4) + (3/7)x^(7/3) + C

Explanation:

To find the antiderivative of g(x) = x^(3/4) + x^(4/3):

Using the power rule for integration:

1. For the term x^(3/4):

∫ x^(3/4) dx = (4/7)x^(7/4)

2. For the term x^(4/3):

∫ x^(4/3) dx = (3/7)x^(7/3)

Combining the antiderivatives of the two terms:

∫ (x^(3/4) + x^(4/3)) dx = (4/7)x^(7/4) + (3/7)x^(7/3) + C