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Calculus of Powers

Review question

Can we find the area inside a straight line, a parabola and the x-axis?
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Ref: R7444

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Question

The figure shows the curve \(y = x^2\) and the straight line \(2x + y = 15\). Find

the co-ordinates of \(P\) and \(Q\),
the area of the shaded region.

A plot of the curve $y = x^2$ and the line $2x + y = 15$ with $-8.5 \le x \le 8.5$. The point in the first quadrant at which the curve and line cross is denoted by $P$. The $x$-intercept of the line is denoted by $Q$. The shaded region is the region beneath both the curve and line and between the origin and $Q$.