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Core Pure: further calculus

Quick questions on Improper integrals: infinite limits, unbounded integrands and convergence - OCR A-Level Further Maths A

2short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is q1?
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Evaluate ∫2∞1x3 dx\displaystyle\int_2^{\infty}\dfrac{1}{x^3}\,dx. [3 marks]
What is q2?
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State, with a reason, whether ∫1∞1x dx\displaystyle\int_1^{\infty}\dfrac{1}{x}\,dx converges. [2 marks]

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