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| # h3macaar1 |
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Calculate the area enclosed by the curve y = x2+1, the y-axis and the lines, y=2,y=3 for the portion in the first quadrant only. |
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Strategy -
the rule "Must have" of Mr.Zhang ® Find the area ; → (1) To calculate area A, x must be expressed in terms of y for the intregation. |
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| Solution | We have ; | |
| y | = | x2 + 1 |
| x2 | = | y - 1 |
| x | = | (y-1) 1/2 |
| We bring the equation(1) to find the required area; |  |
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| = |  |
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| = |  |
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| = |
2
3
|
(2)3/2 - |
2
3
|
(1)3/2 | |
| = |
2
3
|
(2√2) - |
2
3
|
||
| = |
2
3
|
(2√2 - 1) | |||
| Ans. The area is |
2
3
|
(2√2 - 1) units2 |
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