Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

$${\int_{-4}^{4}} (10x^{9} + 7x^{5}) dx$$

I got 2097152 as the answer, but the website I'm doing my homework on says it is wrong. Just need a little help here.

share|improve this question
    
You performed your computation incorrectly. In any case, there is a simpler way... –  copper.hat Feb 2 '13 at 6:17
add comment

4 Answers

Observe the function is odd (meaning $f(-x)=-f(x)$), so try splitting the integral $$\int_{-4}^4 f(x)dx=\int_{-4}^0 f(x)dx+\int_0^4f(x)dx=\int_0^4f(-x)dx+\int_0^4f(x)dx.$$ What happens next?

share|improve this answer
add comment

Although the odd function property is a better way: Just to add to the possible solutions: \begin{align} \int_{-4}^410x^9+7x^5&=\left[x^{10}+ \dfrac{7x^6}{6} \right] _{-4}^4\\ &=\left[4^{10}+ \dfrac{7\times 4^6}{6} \right]-\left[(-4)^{10}+ \dfrac{7(-4)^6}{6} \right]\\ \end{align}

\begin{align} &=\left[4^{10}+ \dfrac{7\times 4^6}{6} \right]-\left[(4)^{10}+ \dfrac{7(4)^6}{6} \right] \\&=0\end{align}

share|improve this answer
add comment

Note that the function is an odd function and you integrating it from $-4$ to $4$. In general, if $f(x)$ is odd and integrable, we have $$\int_{-a}^a f(x) dx = 0$$where $a \in \mathbb{R}$.

share|improve this answer
add comment

Note that you are solving $\int_{-a}^a f(x) dx$ where $f$ is odd. What does that say about $\int_{-a}^0 f(x) dx$ and $\int_{0}^a f(x) dx$?

share|improve this answer
    
I messed up. I totally forgot about odd function. thank you! –  Ak47 Feb 2 '13 at 6:39
    
I just did the integration and noticed at the end. Hindsight is 20-20. –  copper.hat Feb 2 '13 at 6:43
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.