Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The diagram displays part of the curve with equation $y = \frac{12}{\sqrt[3]{2x + 1}}$. The point $A$ on the curve has coordinates $(\frac{7}{2}, 6)$.
(a)[4]

Determine the equation of the tangent to the curve at $A$. Write your answer in the form $y = mx + c$.

(b)[4]

Determine the area of the region enclosed by the curve and the lines $x = 0$, $x = \frac{7}{2}$ and $y = 0$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Differentiate to obtain an expression of the form $k_1(2x+1)^{-4/3}$

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