Area under curve
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Given a function defined on an interval, the area under the curve and above the x-axis can be calculated using the definite integral \( A=\int_a^b f(x) d x\) Where:
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Activity – 1: Determining the area under a curve that extends both above and below the x-axis. |
Interactive graph
Use the sliders to adjust the parameters to understand the transformation.
Practice question:
Question No: 1 [ Maximum Mark: 7 ] (Do not use GDC)
| Find the area under the curve \( y=\sqrt{(x) }\) above \( x-axis \) between the limits \(x=2 \) \( x=3\) | |||
| Answer : \( Area \) | |||
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Activity – 2: Determining the area under a curve that extends both above and below the x-axis. |
Interactive graph
Use the sliders to adjust the parameters to understand the transformation.
Practice question:
Question No: 2 [ Maximum Mark: 7 ] (Do not use GDC)
| Find the area under the curve \( y=e^{-x}-1 \) above \( x-axis \) between the limits \(x=1 \) \( x=5\) | |||
| Answer : \( Area = \left(\frac{1}{e^5}-\frac{1}{e}+4\right) = 3.64\) | |||
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Activity 3: Determining the area under a curve that extends both above and below the x-axis. |
Interactive graph
Use the sliders to adjust the parameters to understand the transformation.
Practice question:
Question No: 3 [ Maximum Mark: 7 ] (Do not use GDC)
| Find the area under the curve \( y=x^3-4 x\) above \( x-axis \) between the limits \(x=2 \) \( x=3\) | |||
| Answer : \( Area =40 square units \) | |||
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