AP EAMCET · Maths · Indefinite Integration
\(\int\left(\sqrt{\frac{a+x}{a-x}}+\sqrt{\frac{a-x}{a+x}}\right) d x\) is equal to
- A \(2 \sin ^{-1}\left(\frac{x}{a}\right)+C\)
- B \(2 a \sin ^{-1}\left(\frac{x}{a}\right)+C\)
- C \(2 \cos ^{-1}\left(\frac{x}{a}\right)+C\)
- D \(2 a \cos ^{-1}\left(\frac{x}{a}\right)+C\)
Answer & Solution
Correct Answer
(B) \(2 a \sin ^{-1}\left(\frac{x}{a}\right)+C\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Let } I=\int\left(\sqrt{\frac{a+x}{a-x}}+\sqrt{\frac{a-x}{a+x}}\right) d x \\ & \text { Put } x=a \cos 2 \theta \Rightarrow d x=-2 a \sin 2 \theta d \theta \\ & \therefore I=-\int\left(\sqrt{\frac{a+a \cos 2 \theta}{a-a \cos 2 \theta}}+\sqrt{\frac{a-a…
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 the smallest circle through the points of intersection of \(x^2+y^2=a^2\) and \(x \cos \alpha+y \sin \alpha=p, 0 < p < a\) is \(x^2+y^2-a^2+\lambda(x \cos \alpha+y \sin \alpha-p)=0\) then \(\lambda=\)AP EAMCET 2025 Medium
- \(\int \sqrt{x+\sqrt{x^2+2}} d x=\)AP EAMCET 2022 Easy
- The semi-vertical angle of a right circular cone is \(45^{\circ}\). If the radius of the base of the cone is measured as 14 cm with an error of \(\left(\frac{\sqrt{2}-1}{11}\right) \mathrm{cm}\), then the approximate error in measuring its total surface area is (in sq. cm )AP EAMCET 2024 Easy
- If \(f(x)=x^{\operatorname{Sec}^{-1} x}\), then \(f^{\prime}(2)=\)AP EAMCET 2025 Medium
- Let \(f(x)=x^2+\frac{1}{x^2}\) and \(g(x)=x-\frac{1}{x}\) for \(x \in R-\{-1,0,+1\}\), then the local minimum of \(\frac{f(x)}{g(x)}\) isAP EAMCET 2022 Medium
- The coefficient of variation of \(9,3,11,5,7\), isAP EAMCET 2019 Easy
More PYQs from AP EAMCET
- \(\int \frac{x^4+1}{1+x^6} d x=\)AP EAMCET 2018 Easy
- Let \(\mathrm{X}\) - axis be the transverse axis and \(\mathrm{Y}\)-axis be the conjugate axis of a hyperbola \(\mathrm{H}\). Let \(\mathrm{x}^2+\mathrm{y}^2=16\) be the director circle of \(\mathrm{H}\). If the perpendicular distance from the centre of \(\mathrm{H}\) to its latus rectum is \(\sqrt{34}\) then \(\mathrm{a}+\mathrm{b}=\)AP EAMCET 2023 Easy
- Assertion (A) 16th group elements have higher ionisation enthalpy values than 15th group elements in the corresponding periods.
Reason (R) 15th group elements have half-filled stable electronic configurations.AP EAMCET 2022 Medium - A certain vector in the \(x y\)-plane has an \(x\)-component of \(4 \mathrm{~m}\) and a \(y\)-component of \(10 \mathrm{~m}\). It is then rotated in the \(x y\)-plane so that its \(x\)-component is doubled. Then its new \(y\)-component is (approximately)AP EAMCET 2011 Easy
- Find the equations of the tangents drawn to the circle at the points where the line meets it.AP EAMCET 2021 Easy
- Which of the following statement is incorrect?AP EAMCET 2021 Easy