TS EAMCET · Maths · Indefinite Integration
\(\int \tan ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right) d x\) is equal to
- A \(\frac{1}{2}\left(x \cos ^{-1} x-\sqrt{1-x^2}\right)+c\)
- B \(\frac{1}{2}\left(x \cos ^{-1} x+\sqrt{1-x^2}\right)+c\)
- C \(\frac{1}{2}\left(x \sin ^{-1} x-\sqrt{1-x^2}\right)+c\)
- D \(\frac{1}{2}\left(x \sin ^{-1} x+\sqrt{1-x^2}\right)+c\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{2}\left(x \cos ^{-1} x-\sqrt{1-x^2}\right)+c\)
Step-by-step Solution
Detailed explanation
Let \(I=\int \tan ^{-1} \sqrt{\frac{1-x}{1+x}} d x\) Put \(x=\cos 2 \theta\)…
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
- The number of all possible three letter words that can be formed by choosing three letters from the letters of the word FEBRUARY so that a vowel always occupies the middle place isTS EAMCET 2025 Medium
- If the distance between the points \((a \cos \theta, a \sin \theta)\) and \((a \cos \phi, a \sin \phi)\) is \(2 a\), then \(\theta\) is equal toTS EAMCET 2004 Easy
- \((1,-2,1)\) is a point on a plane \(\pi\) and \(\pi\) is parallel to the plane \(x-y-z=0\). If the equation of \(\pi\) is \(a x+b y+c z-2\) \(=0\), then \(b-2 c=\)TS EAMCET 2023 Easy
- If 4 letters are selected at random from the letters of the word PROBABILITY, then the probability of getting a combination of letters in which atleast one letter is repeated isTS EAMCET 2024 Medium
- The locus of the mid points of the chords of the circle drawn from a point on it isTS EAMCET 2021 Easy
- If \(y=m x+1\) is tangent to the parabola \(y^2=4 x\), then \(m=\)TS EAMCET 2019 Easy
More PYQs from TS EAMCET
- A cylindrical resistor of radius \(7.0 \mathrm{~mm}\) and length 4.0 \(\mathrm{cm}\) is made of material that has a resistivity of \(10^{-6} \Omega . \mathrm{m}\). If the energy is dissipated at rate \(1.54 \mathrm{~W}\) in the resistor, then the current density isTS EAMCET 2022 Medium
- \(\int_{\frac{-3}{4}}^{\frac{\pi-6}{8}} \log (\sin (4 x+3)) d x=\)TS EAMCET 2024 Medium
- Ratio of translational degrees of freedom to rotational degrees of freedom of a polyatomic linear gas molecule isTS EAMCET 2023 Hard
- Assertion (A) The boiling points of noble gases increases from He to Xe. Reason (R) The interatomic van der Waals' attractive forces increases from \(\mathrm{He}\) to \(\mathrm{Xe}\). The correct answer isTS EAMCET 2012 Easy
- \(\mathrm{A}(2,0), \mathrm{B}(0,2), \mathrm{C}(-2,0)\) are three points. Let \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) be the perpendicular distances from a variable point P on to the lines \(\mathrm{AB}, \mathrm{BC}\) and CA respectively. If \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) are in arithmetic progression, then the locus of P isTS EAMCET 2025 Hard
- If the angle between the circles \(x^2+y^2-2 x+\mathrm{k} y+1=0\) and \(x^2+y^2-\mathrm{k} x-2 y+1=0\) is \(\operatorname{Cos}^{-1}\left(\frac{1}{4}\right)\) and \(\mathrm{k} < 0\) then the point which lies on the radical axis of the given circles isTS EAMCET 2025 Medium