The value of ∫dx1-x is ______. - Mathematics and Statistics

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MCQ
Fill in the Blanks

The value of `int dx/(sqrt(1 - x))` is ______.

Options

  • `2sqrt(1 - x) + c`

  • `-2sqrt(1 - x) + c`

  • `sqrtx + c`

  • x + c

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Solution

The value of `int dx/(sqrt(1 - x)) "is"  underlinebb(-2sqrt(1 - x) + c)`.

Explanation:

The integral in question can be approached by considering a simple u-substitution where u = 1 − x. Then, du = − dx or − du = dx, which transforms the integral into:

`int ​(−du)/u​`

This is a standard integral that evaluates to:

`−2sqrtu ​+ "C"`

Substituting back for u, we get:

`−2sqrt(1 − x​) + "C"`

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2023-2024 (March) Official

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