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: $\int_{0}^{\frac{\pi }{2}}{\cos (\sin x)dx}\lt 0\lt \int_{0}^{\frac{\pi }{2}}{\sin (\sin x)dx}$
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: $\int_{0}^{\frac{\pi }{2}}{\cos (\sin x)dx}\lt 0\lt \int_{0}^{\frac{\pi }{2}}{\sin (\sin x)dx}$
举一反三
- 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
- 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: $\int_{-\pi}^\pi \cos nx \cos mx dx =\pi,\quad m\neq n$
- Solve $ \frac{1}{\pi}\int_0^{\frac{\pi}{2}}\sin^4{x}dx=$ :<br/>______
- Solve $n \in \mathbb{N}, \int_0^{\frac{\pi}{2}}(\sin^n{x}-\cos^n{x})dx=$ :<br/>______
- $\int \sin^3 x \cos x dx = $ A: $\frac{\sin^4 x}{4} +C$ B: ${\sin^4 x} +C$ C: $\frac{\cos^4 x}{4} +C$ D: $\frac{\cos^4 x}{4} +C$