AI generatedAlgebraGCSE Higher

Estimating an area under a graph

Use suitable rectangles or trapezia.

  • Check axis labels and scales before reading values.
  • Use key points and the correct curve shape. Join a curved graph smoothly.
  • An asymptote is approached; do not join separate branches across it.

Example 1

Estimate the area under the curve from to using four equal-width trapezia.

Coordinate graph12345246810120
Four strips across a width of 4 give strip width 1.The first and last heights appear once; interior heights appear twice.

Example 2

Estimate the area under the curve from to using four equal-width trapezia.

Coordinate graph1234551015200
Four strips across a width of 4 give strip width 1.The first and last heights appear once; interior heights appear twice.

Your turn

Question 1

Estimate the area under the curve from to using four equal-width trapezia.

Coordinate graph123455101520250
Check answer
Four strips across a width of 4 give strip width 1.The first and last heights appear once; interior heights appear twice.
Question 2

Estimate the area under the curve from to using four equal-width trapezia.

Coordinate graph1234524681012140
Check answer
Four strips across a width of 4 give strip width 1.The first and last heights appear once; interior heights appear twice.
Question 3

Estimate the area under the curve from to using four equal-width trapezia.

Coordinate graph1234551015200
Check answer
Four strips across a width of 4 give strip width 1.The first and last heights appear once; interior heights appear twice.
Question 4

Estimate the area under the curve from to using four equal-width trapezia.

Coordinate graph12345510152025300
Check answer
Four strips across a width of 4 give strip width 1.The first and last heights appear once; interior heights appear twice.
Question 5

Estimate the area under the curve from to using four equal-width trapezia.

Coordinate graph1234524681012140
Check answer
Four strips across a width of 4 give strip width 1.The first and last heights appear once; interior heights appear twice.
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