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Question
Area bounded by the curve y = x3, the x-axis and the ordinates x = −2 and x = 1 is ______.
Options
−9
`(-15)/4`
`15/4`
`17/4`
Solution
Area bounded by the curve y = x3, the x-axis and the ordinates x = −2 and x = 1 is `underline(17/4)`.
Explanation:
The required area is the shaded region, as shown in the graph.
∴ Required area `= |int_-2^0 x^3 dx| + int_0^1 x^3 dx`
`= |[x^4/4]|_-2^0 + [x^4/4]_0^1`
`= |(0 - 16/4)| + (1/4 - 0)`
`= 16/4 + 1/4`
`= 17/4` square units
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