# Integration

$$u_{10}=integration lim 0 to pi/2 x^10sinxdx , then the value of u_{10}+90u_{8}$$ is equal to

Note by Anirudha Nayak
4 years, 6 months ago

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Let $$\displaystyle u_{10} = \int_{0}^{\frac{\pi}{2}}x^{10}\cdot \sin xdx$$

Using Integration by parts, we get

$$\displaystyle u_{10} =0+ 10\int_{0}^{\frac{\pi}{2}}x^9\cos xdx$$

$$\displaystyle u_{10} = 10\cdot \frac{\pi^9}{2^9} - 90u_{8}$$

$$\displaystyle u_{10}+90u_{8} = 10\cdot \frac{\pi^9}{2^9}$$

- 4 years, 6 months ago