Definite integral with complex result?

[Painguy]

Homework Statement

∫ 3+ x√x from -1 to 4

Homework Equations

The Attempt at a Solution

∫ 3+ x√x from -1 to 4 = 3x+(2(x^5/2))/5 evaluated from -1 to 4

(12 + (2(4^5/2))/5) +(3 +(2(-1)^5/2)/5) ?

15+64/5 +(2(-1^(5/2))/5)

139/5 -(2(-1^(5/2)))/5

139/5 -2i/5

is that right?

 

[Sherry Darlin]

Homework Statement

∫ 3+ x√x from -1 to 4

Homework Equations

The Attempt at a Solution

∫ 3+ x√x from -1 to 4 = 3x+(2(x^5/2))/5 evaluated from -1 to 4

(12 + (2(4^5/2))/5) +(3 +(2(-1)^5/2)/5) ?

15+64/5 +(2(-1^(5/2))/5)

139/5 -(2(-1^(5/2)))/5

139/5 -2i/5

is that right?

Yes:

http://www.wolframalpha.com/input/?i=integrate+3+++x*sqrt(x)+from+-1+to+4

 

[Mark44]

Homework Statement

∫ 3+ x√x from -1 to 4

Because of the term with the square root, the integrand is defined only for x ≥ 0. What is the complete statement of the problem?

Although there is a version of the square root function whose domain includes negative numbers, this is usually not presented in calculus courses.

Homework Equations

The Attempt at a Solution

∫ 3+ x√x from -1 to 4 = 3x+(2(x^5/2))/5 evaluated from -1 to 4

(12 + (2(4^5/2))/5) +(3 +(2(-1)^5/2)/5) ?

15+64/5 +(2(-1^(5/2))/5)

139/5 -(2(-1^(5/2)))/5

139/5 -2i/5

is that right?