Evaluating Integral ∫(1+2x³) dx from 0 to 5 for Answer 635/2

[jimen113]

Homework Statement

\int^{5}_{0} 1+2x^{3}

Homework Equations

answer is: 635/2

The Attempt at a Solution

Integrating the function I get this: 1/2(x+x^{}4)
My answer when evaluating the limits =1/2(630)

 

[Hootenanny]

Homework Statement

\int^{5}_{0} 1+2x^{3}

Homework Equations

answer is: 635/2

The Attempt at a Solution

Integrating the function I get this: 1/2(x+x^{}4)

You might want to re-check your integral. What is:

\int 1 dx

 

[arildno]

Why should an anti-derivative of 1 be 1/2x, rather than just x?

 

[jimen113]

\int1=x
\int 2x^3 = \frac{x^4}{2},
1/2\intx+x^4
I took (1/2) out of the \frac{X^{4}}{2}
(So, maybe I can't do that, I should leave it and evaluate at the limits using (x^4/2)?

 

[Hootenanny]

\int1=x
\int 2x^3 = \frac{x^4}{2},
1/2\intx+x^4
I took (1/2) out of the \frac{X^{4}}{2}
(So, maybe I can't do that, I should leave it and evaluate at the limits using (x^4/2)?

Note that:

x+\frac{1}{2}x^4 \neq \frac{1}{2}\left(x+x^4\right)

So yes, you need to evaluate:

\left.\left(x+\frac{1}{2}x^4\right)\right|_0^5

 

[jimen113]

I see where I went wrong, thank you for your help!