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Area Under a Graph
Chapter summary, hard words and model exam answers for ICSE Class 10 Hindi.
Free online summary and notes (ICSE Class 10 Hindi). Read it here, no PDF download needed.
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Mathematics · CBSE 10 · ICSE 10 · GCSE (AQA, Edexcel, OCR)
Summary
Height is speed and width is time, so area (height × width) is speed × time = distance. A straight-line graph makes triangles, rectangles or trapeziums you can measure exactly.
Triangle = ½ × base × height, rectangle = length × width, trapezium = ½(a + b) × h. Add every section to get the total distance.
Area ≈ ½h(first + last + 2 × middles), where h is the strip width. More strips give a closer estimate, but it is still an approximation.
Area below the time axis means the object moved backwards. Distance = total area; displacement = area above − area below.
Hard words & meanings
| velocity-time graph | a graph with time on the x-axis and velocity on the y-axis; its area gives distance |
| area under the graph | the region between the line and the time axis; equals distance for a v-t graph |
| trapezium | a four-sided shape with one pair of parallel sides; area = ½(a + b) × h |
| trapezium rule | a method estimating area under a curve by summing thin trapezium strips |
| strip width (h) | the equal width of each vertical strip in the trapezium rule; smaller h is more accurate |
| displacement | net distance from the start counting direction; area above minus area below the axis |
| distance | the total path length; the sum of all areas, ignoring sign |
| gradient | the steepness of a line; on a v-t graph the gradient is acceleration |
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