关于三角函数系，下列说法正确的是（$\quad$）
A: $\int_{-\pi}^\pi \cos nx dx =1$
B: $\int_{-\pi}^\pi \cos nx \sin nx dx =0$
C: $\int_{-\pi}^\pi \cos nx \sin mx dx =\pi,\quad m=n$
D: $\int_{-\pi}^\pi \cos nx \cos mx dx =\pi,\quad m\neq n$
A: $\int_{-\pi}^\pi \cos nx dx =1$
B: $\int_{-\pi}^\pi \cos nx \sin nx dx =0$
C: $\int_{-\pi}^\pi \cos nx \sin mx dx =\pi,\quad m=n$
D: $\int_{-\pi}^\pi \cos nx \cos mx dx =\pi,\quad m\neq n$
举一反三
- 8. 下列不等式正确的是 A: $0\lt \int_{0}^{\frac{\pi }{2}}{\sin (\sin x)dx}\lt \int_{0}^{\frac{\pi }{2}}{\cos (\sin x)dx}$ B: $0\lt \int_{0}^{\frac{\pi }{2}}{\cos (\sin x)dx}\lt \int_{0}^{\frac{\pi }{2}}{\sin (\sin x)dx}$ C: $\int_{0}^{\frac{\pi }{2}}{\sin (\sin x)dx}\lt 0\lt \int_{0}^{\frac{\pi }{2}}{\cos (\sin x)dx}$ D: $\int_{0}^{\frac{\pi }{2}}{\cos (\sin x)dx}\lt 0\lt \int_{0}^{\frac{\pi }{2}}{\sin (\sin x)dx}$
- 函数\(f(x) = x^2,\; x \in [-\pi,\pi]\)的Fourier级数为 A: \(\frac{\pi^2}{3}+4\Sigma_{n=1}^{\infty} \frac{(-1)^n}{n^2} \sin nx ,\; x \in [-\pi,\pi]\) B: \(\frac{\pi^2}{3}+4\Sigma_{n=1}^{\infty} \frac{(-1)^n}{n^2} \cos nx ,\; x \in [-\pi,\pi]\) C: \(\frac{2\pi^2}{3}+4\Sigma_{n=1}^{\infty} \frac{(-1)^n}{n^2} \sin nx ,\; x \in [-\pi,\pi]\) D: \(\frac{2\pi^2}{3}+4\Sigma_{n=1}^{\infty} \frac{(-1)^n}{n^2} \cos nx ,\; x \in [-\pi,\pi]\)
- 设$f(x)$是$[-1,1]$上的连续函数, 则$\int_{-\pi}^{\pi}\sin x(\sin x+f(\cos x))dx=$ A: $0$ B: $2$ C: $\pi$ D: 以上都不对
- Solve $n \in \mathbb{N}, \int_0^{\frac{\pi}{2}}(\sin^n{x}-\cos^n{x})dx=$ :<br/>______
- 已知“syms s t r; I1=int(int(int(r.^4*sin(s),r,0,2*cos(s)),s,0,pi/3),t,0,2*pi); I2=int(int(int(r.^4*sin(s),r,0,1), s,pi/3,pi),t,0,2*pi); I=I1+I2”中,则下列说法正确的是【】