`int_0^1 x(root(3)(x) + root(4)(x)) dx` Evaluate the integral

Textbook Question

Chapter 5, 5.4 - Problem 31 - Calculus: Early Transcendentals (7th Edition, James Stewart).
See all solutions for this textbook.

1 Answer | Add Yours

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

 

You need to evaluate the definite integral, such that:

`int_0^1 x(root(3) x + root(4) x)dx = int_0^1 (x^(1+1/3) + x^(1+1/4))dx`

`int_0^1 x(root(3) x + root(4) x)dx = ((x^(2+1/3))/(2+1/3) + (x^(2+1/4))/(2+1/4))|_0^1`

`int_0^1 x(root(3) x + root(4) x)dx = ((3/7)x^2root(3)x + (4/9)x^2root(4)x)|_0^1`

`int_0^1 x(root(3) x + root(4) x)dx = 3/7 + 4/9`

`int_0^1 x(root(3) x + root(4) x)dx = 55/63`

Hence, evaluating the definite integral yields

`int_0^1 x(root(3) x + root(4) x)dx = 55/63.`

We’ve answered 318,980 questions. We can answer yours, too.

Ask a question