The region R is bounded by the curve y = 2x and the x-axis for 0 x 4. What is the area of R?

B1: Identify the area under the straight-line graph as a triangle or use _0^4 2x \, dx. A1: 16. Accept 12 4 8 = 16 or correct integration. Do not award for using the height as 4 instead of 8, or for 2x \, dx evaluated incorrectly.

A-Level Mathematics: Areas Under Curves questions

Q: The curve has equation y=x^2-4x. Find the exact area between the curve and the x-axis from x=0 to x=4.

A1: 323. Accept equivalent exact forms such as 10 23 if written exactly. Do not award for using the signed integral without recognising the curve is below the x-axis on part of the interval, or for 163 from integrating x^2-4x without taking absolute area.

Q: The curve y=x^2 and the x-axis enclose a region from x=0 to x=2. What is the area of this region?

B1: 83. Accept: 2.666 . Do not award for the value of the integral without the area interpretation if a negative answer is given.

4 exam-style questions on areas under curves, each with a full mark scheme. Written for Edexcel. These are Kepler’s own questions, not reproduced past papers.

Question 11 mark

The curve has equation $y=x{^2}-4x$ . Find the exact area between the curve and the $x$ -axis from $x=0$ to $x=4$ .

Show the mark scheme

A1: $\frac{32}{3}$ . Accept equivalent exact forms such as $10\frac{2}{3}$ if written exactly. Do not award for using the signed integral without recognising the curve is below the $x$ -axis on part of the interval, or for $\frac{16}{3}$ from integrating $x{^2}-4x$ without taking absolute area.

Question 21 mark

The region $R$ is bounded by the curve $y = 2x$ and the $x$ -axis for $0 \leq x \leq 4$ . What is the area of $R$ ?

Show the mark scheme

B1: Identify the area under the straight-line graph as a triangle or use $\int_{0}{^4} 2x \, dx$ . A1: $16$ . Accept $\frac{1}{2} \times 4 \times 8 = 16$ or correct integration. Do not award for using the height as $4$ instead of $8$ , or for $\int 2x \, dx$ evaluated incorrectly.

Question 31 mark

The curve $y=x{^2}$ and the $x$ -axis enclose a region from $x=0$ to $x=2$ . What is the area of this region?

Show the mark scheme

B1: $\frac{8}{3}$ . Accept: $2.666\ldots$ . Do not award for the value of the integral without the area interpretation if a negative answer is given.

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A-Level Mathematics: Areas Under Curves questions

4 exam-style questions on areas under curves, each with a full mark scheme. Written for Edexcel. These are Kepler’s own questions, not reproduced past papers.

Question 11 mark

The curve has equation $y=x{^2}-4x$ . Find the exact area between the curve and the $x$ -axis from $x=0$ to $x=4$ .

Show the mark scheme

Question 21 mark

The region $R$ is bounded by the curve $y = 2x$ and the $x$ -axis for $0 \leq x \leq 4$ . What is the area of $R$ ?

Show the mark scheme

Question 31 mark

The curve $y=x{^2}$ and the $x$ -axis enclose a region from $x=0$ to $x=2$ . What is the area of this region?

Show the mark scheme

B1: $\frac{8}{3}$ . Accept: $2.666\ldots$ . Do not award for the value of the integral without the area interpretation if a negative answer is given.

Get these marked

Start revising for free