TS EAMCET · Maths · Definite Integration
\(\int_0^1 \sqrt{\frac{1-x}{1+x}} d x\) is equal to
- A \(\frac{\pi}{2}-1\)
- B \(\frac{\pi}{2}+1\)
- C \(\pi-1\)
- D \(\frac{3 \pi}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{2}-1\)
Step-by-step Solution
Detailed explanation
Let \[ \begin{aligned} I & =\int_0^1 \sqrt{\frac{1-x}{1+x}} d x \\ & =\int_0^1 \sqrt{\frac{1-x}{1+x}} \times \sqrt{\frac{1-x}{1-x}} d x \\ & =\int_0^1 \frac{1-x}{\sqrt{1-x^2}} d x \\ & =\int_0^1 \frac{1}{\sqrt{1-x^2}} d x-\int_0^1 \frac{x}{\sqrt{1-x^2}} d x \end{aligned} \]…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If and are the three vertices of a parallelogram , then the angle between its diagonal through and the side isTS EAMCET 2019 Medium
- The sum of the coefficients of \(x^{-3 / 2}\) and \(x^3\) in the expansion of \(\sqrt{3+x}+\sqrt{5+x}\) when \(3 < x < 5\), isTS EAMCET 2020 Hard
- All the letters of the word 'INDEED' are taken and permuted in all possible ways to form distinct 6 letter strings (words with or without meaning). If they are listed in dictionary order, then the rank position of the string 'NIDDEE' isTS EAMCET 2023 Medium
- If \(l\) is the maximum value of \(-3 x^2+4 x+1\) and \(m\) is the minimum value of \(3 x^2+4 x+1\), then the equation of the hyperbola having foci at \((l, 0),(7 \mathrm{~m}, 0)\) and eccentricity as 2 isTS EAMCET 2025 Hard
- If \((4,3)\) and \((1,-2)\) are the end points of a diagonal of a square, then the equation of one of its sides isTS EAMCET 2024 Easy
- If the position vectors of three points respectively are and , then the perpendicular distance of the point from the line isTS EAMCET 2018 Medium
More PYQs from TS EAMCET
- If \(\Delta_1=\left|\begin{array}{lll}1 & a^2 & a^3 \\ 1 & b^2 & b^3 \\ 1 & c^2 & c^3\end{array}\right|\) and \(\Delta_2=\left|\begin{array}{lll}b c & b+c & 1 \\ c a & c+a & 1 \\ a b & a+b & 1\end{array}\right|\), then \(\frac{\Delta_1}{\Delta_2}=\)TS EAMCET 2018 Medium
- If \(x=\frac{1}{2}\left(\sqrt{7}+\frac{1}{\sqrt{7}}\right)\), then \(\frac{\sqrt{x^2-1}}{x-\sqrt{x^2-1}}\) is equal toTS EAMCET 2008 Medium
- Dihydrogen can be prepared by which of the following reactions. (I) Reaction of granulated \(\mathrm{Zn}\) with dil. \(\mathrm{HCl}\) (II) Reaction of Zn with aq. \(\mathrm{NaOH}\) (III) By heating calcium hydrogen carbonateTS EAMCET 2020 Medium
- The chemical name of calgon isTS EAMCET 2023 Easy
- The solution of \(\frac{d y}{d x}=\left(\frac{x}{y}\right)^{-1 / 3}\) isTS EAMCET 2002 Medium
- For any fixed distance, the electromagnetic force between two protons is \(10^n\) times of the gravitational force between them. Then \(\mathrm{n}=\)TS EAMCET 2025 Medium