Find the area of the region bounded by the curve $y = x^2$ and the line $y = x$.

Find the area of the region bounded by the curve y = x² and the line y = x.

Example · Example 7

y = x^2

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The curves meet at $x=0$ and $x=1$ , with the line above the parabola in between.

Setting $x^2=x$ gives $x^2-x=0 \Rightarrow x(x-1)=0$ , so the curves meet at $x=0$ and $x=1$ . Testing $x=0.5$ : the line gives $y=0.5$ and the parabola gives $y=0.25$ , so the line $y=x$ lies above the parabola $y=x^2$ throughout $(0,1)$ . The enclosed area is …

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Q.Find the area of the region bounded by the curve $y = x^2$ and the line $y = x$ .

Concept understanding — Area between Two Curves

Q.Find the area of the region bounded by the curve y=x2y = x^2y=x2 and the line y=xy = xy=x.

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Q.Find the area of the region bounded by the curve $y = x^2$ and the line $y = x$ .

Unlock everything free for 14 days