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$$\int$$x+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$$\int$$x+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!