Quick questions on Integration: the reverse process and areas under curves - WJEC A-Level Maths

4short 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 finding a curve from its gradient?

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If you know

\dfrac{dy}{dx}

and one point on the curve, integrate to get a family of curves

y = F(x) + c

, then substitute the point to pin down

c

What is q1?

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Find

\displaystyle\int (6x^2 - 4x + 5)\,dx

. [3 marks]

What is q2?

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Evaluate

\displaystyle\int_0^4 \sqrt{x}\,dx

. [3 marks]

What is q3?

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A curve has gradient

\dfrac{dy}{dx} = 2x + 1

and passes through

(2, 7)

. Find

y

. [3 marks]

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