2.6.2.30 Trigonometric Fourier series

condition: The coefficient \( a_{15} \) of the Fourier series expansion on the segment \( [-4 ; 4] \) of the function \( f(x)=-5 x^{2}+5 \) is calculated by the formula? 1) \( \frac{1}{4} \int_{-4}^{4}\left(-5 x^{2}+5\right) \sin \left(\frac{15 \pi x}{4}\right) d x \) 2) \( a_{15}=0 \) 3) \( \frac{1}{4} \int_{-4}^{4}\left(-5 x^{2}+5\right) \cos \left(\frac{15 \pi x}{4}\right) d x \) 4) \( \frac{2}{4} \int_{0}^{4}\left(-5 x^{2}+5\right) \cos \left(\frac{15 \pi x}{4}\right) d x \) 5) \( \frac{2}{4} \int_{0}^{4}\left(-5 x^{2}+5\right) \sin \left(\frac{15 \pi x}{4}\right) d x \)