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Calculus

Quick questions on Definite integrals and areas explained: H2 Mathematics Calculus

6short 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 area under a curve?
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For f(x)≥0\mathrm{f}(x) \geq 0 on [a,b][a, b], the area between the curve and the xx-axis is ∫abf(x) dx\displaystyle\int_a^b \mathrm{f}(x)\,dx.
What are area between two curves?
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If the curve y=f(x)y = \mathrm{f}(x) lies above y=g(x)y = \mathrm{g}(x) on [a,b][a, b], the enclosed area is
What are wrong order in area between curves?
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Use upper minus lower; reversing gives a negative result.
What is q1?
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Evaluate ∫13(2x+1) dx\displaystyle\int_1^3 (2x + 1)\,dx. [2 marks]
What is q2?
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Find the area between y=x2y = x^2 and the xx-axis from x=0x = 0 to x=3x = 3. [2 marks]
What is q3?
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State how to find the area enclosed between two curves. [2 marks]

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