Compute $\int_{-R}^{R} \frac{\sin x}{9+x^{4}} d x$ .
A) $\frac{2 \cos R}{9 R+R^{5}}$
B) $\frac{3 \cos \left(9+R^{4}\right)}{R^{3}}$
C) $\frac{1}{3\left(9+R^{4}\right)}$
D)0

Question

Quizplus · Accepted Answer

The integral of an odd function over a symmetric interval around zero is zero. Since $\frac{\sin x}{9+x^{4}}$ is an odd function (because $\sin x$ is odd and $9+x^4$ is even), its integral from $-R$ to $R$ is 0.

Compute ∫−RRsin⁡x9+x4dx\int_{-R}^{R} \frac{\sin x}{9+x^{4}} d x∫−RR​9+x4sinx​dx A) 2cos⁡R9R+R5\frac{2 \cos R}{9 R+R^{5}}9R+R52cosR​

Compute $\int_{-R}^{R} \frac{\sin x}{9+x^{4}} d x$
A) $\frac{2 \cos R}{9 R+R^{5}}$