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1.8.9 Integration by parts (A-level only)

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Question 42

Given that

∫π6π2xsin⁡x dx=aπ+b \int_{\frac{\pi}{6}}^{\frac{\pi}{2}} x \sin x \, dx = a\pi + b ∫6π​2π​​xsinxdx=aπ+b

find the exact value of aaa and the exact value of bbb.

Fully justify your answer.

[6]

1.8.9 Integration by parts (A-level only) Questions

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