GATE 2016 EC (EC3) – Question 14
The integral $\int_0^1 dx/\sqrt{1-x}$ equals ________.
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Show answer and explanation
Correct answer: 2.0 to 2.0
Explanation
The integrand is singular at x=1, so interpret the integral as an improper limit. An antiderivative is $-2\sqrt{1-x}$.
At upper limit b<1, the integral is $2-2\sqrt{1-b}$. Let b tend to 1 from below to obtain the finite value **2**.