Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The diagram shows a segment of the curve $y = \sqrt{4x + 1} + \frac{9}{\sqrt{4x + 1}}$ together with the minimum point $M$.
(i)[6]

Find expressions for $\frac{dy}{dx}$ and for $\int y\,dx$.

(ii)[3]

Find the coordinates for $M$.

(iii)[3]

The shaded region is enclosed by the curve, the $y$-axis and the line through $M$ parallel to the $x$-axis. Find, showing all necessary working, the area of the shaded region.

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