AP EAMCET · Maths · Definite Integration
\(\int_0^1 \sin \left(2 \tan ^{-1} \sqrt{\frac{1+x}{1-x}}\right) d x\) is equal to :
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{\pi}{2}\)
- D \(\pi\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
Let \(I=\int_0^1 \sin \left(2 \tan ^{-1} \sqrt{\frac{1+x}{1-x}}\right) d x\) Put \(x=\cos \theta \Rightarrow d x=-\sin \theta d \theta\) \(\therefore \quad I=\int_{\pi / 2}^0 \sin \left(2 \tan ^{-1} \sqrt{\frac{1+\cos \theta}{1-\cos \theta}}\right)(-\sin \theta) d \theta\)…
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
- If a line \(\mathrm{L}\) makes angles \(\frac{\pi}{3}\) and \(\frac{\pi}{4}\) with the positive \(\mathrm{X}\)-axis and positive \(\mathrm{Y}\)-axis respectively, then the angle made by \(\mathrm{L}\) with the positive direction of \(\mathrm{Z}\)-axis isAP EAMCET 2023 Easy
- If \(\int \frac{\cos ^3 x}{\sin ^2 x+\sin ^4 x} d x=c-\operatorname{cosec} x-f(x)\), then \(f\left(\frac{\pi}{2}\right)=\)AP EAMCET 2025 Medium
- A number \(n\) is chosen at random from \(\{1,2,3,4, \ldots, 1000\}\). The probability that \(n\) is a number that leaves remainder 1 when divided by 7 , is :AP EAMCET 2006 Hard
- The polar equation of the circle with centre \(\left(2, \frac{\pi}{2}\right)\) and radius 3 units is :AP EAMCET 2006 Medium
- Assertion (A) Order of the differential equations of a family of circles with constant radius is two.
Reason (R) An algebraic equation having two arbitrary constants is general solution of a second order differential equation.AP EAMCET 2022 Easy - \(\int_0^{\pi / 2} \frac{1}{1+\tan ^{2020}(x)} d x=\)AP EAMCET 2020 Medium
More PYQs from AP EAMCET
- If \(13 e^{i \tan ^{-1 \frac{5}{12}}}=a+i b\), then the ordered pair \((\mathrm{a}, \mathrm{b})=\)AP EAMCET 2018 Easy
- The angle between the tangents drawn from the point \((1,2)\) to the ellipse \(3 x^2+2 y^2=5\) isAP EAMCET 2017 Hard
- Match the following
The correct answer isList-I (Molecule) \(\text{List-II (Dipole moment in D)}\) A) \(\mathrm{HCl}\) I) \(1.07\) B) \(\mathrm{NH}_3\) II) \(1.85\) C) \(\mathrm{H}_2\mathrm{O}\) III) \(0.23\) D) \(\mathrm{NF}_3\) IV) \(1.47\) AP EAMCET 2025 Easy - Angle between the lines of intersection of the planes \(x-y=0,2 x+y+z=0\) and \(2 x-z=0, x+y-3 z=0\) isAP EAMCET 2020 Medium
- The frequency of the light emitted when an electron comes down from \(n=4\) to \(n=2\) level in hydrogen atom is \(\frac{3}{7}\) times of the following transition of the Li atomAP EAMCET 2022 Hard
- Identify the most acidic oxide among the following oxides based on their reaction.AP EAMCET 2015 Easy