AP EAMCET · Maths · Indefinite Integration
\(\int \frac{d x}{(1+\sqrt{x}) \sqrt{x-x^2}}=\)
- A \(-2 \sqrt{\frac{1+\sqrt{x}}{1-\sqrt{x}}}+c\)
- B \(-\sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}+c\)
- C \(-2 \sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}+c\)
- D \(2 \sqrt{\frac{1+\sqrt{x}}{1-\sqrt{x}}}+c\)
Answer & Solution
Correct Answer
(C) \(-2 \sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}+c\)
Step-by-step Solution
Detailed explanation
Let \(u=\sqrt{x}\) \(\implies\) \(dx=2u\,du\). \(\int \frac{2u\,du}{(1+u)\sqrt{u^2-u^4}} = \int \frac{2u\,du}{(1+u)u\sqrt{1-u^2}} = \int \frac{2\,du}{(1+u)\sqrt{1-u^2}}\) Let \(u=\sin \theta\) \(\implies\) \(du=\cos \theta\,d\theta\).…
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 \(\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\mathbf{c}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}\) then the magnitude of the projection on \(\mathbf{c}\) of a unit vector that is perpendicular to both \(\mathbf{a}\) and \(\mathbf{b}\) isAP EAMCET 2019 Easy
- If the function \(f(x)=a \sin (x)+\frac{1}{3} \sin (3 x)\) attains maximum value at \(x=\frac{\pi}{3}\), then \(a\) equalsAP EAMCET 2021 Easy
- If \(\left(1+x+x^2\right)^n=a_0+a_1 x+a_2 x^2+\ldots+a_{2 n} x^{2 n}\), then \(a_0+a_2+a_4+\ldots+a_{2 n}=\)AP EAMCET 2017 Medium
- The sum of the distinct values of \(x\) for which the matrix \(A=\left[\begin{array}{lll}1 & 1 & x \\ 1 & x & 1 \\ x & 1 & 1\end{array}\right]\) has no inverse, isAP EAMCET 2023 Easy
- For \(n \in N\), if \(I_n=\int \frac{\sin n x}{\sin x} d x=\frac{2}{n-1} \sin (n-1) x+I_{n-2}\) and \(\int_0^\pi \frac{\sin n x}{\sin x} d x=\frac{k \pi}{2}\), then \(k=\)AP EAMCET 2022 Medium
- When a coin is tossed 6 times, the probability of getting more heads than tails isAP EAMCET 2020 Medium
More PYQs from AP EAMCET
- In \(\triangle A B C, \tan \frac{A}{2}+\tan \frac{B}{2}=\)AP EAMCET 2018 Easy
- If \(f: \mathbf{R} \rightarrow \mathbf{R}\) is defined by
\[
f(x)=\left\{\begin{array}{cl}
x-1, & \text { for } x \leq 1 \\
2-x^2, & \text { for } 1 < x \leq 3 \\
x-10, & \text { for } 3 < x < 5 \\
2 x, & \text { for } x \geq 5
\end{array}\right.
\]
then the set of points of discontinuity of \(f\) isAP EAMCET 2017 Medium - The radius of a circular plate is increasing at the rate of \(0.01 \mathrm{~cm} / \mathrm{s}\) when the radius is \(12 \mathrm{~cm}\). Then, the rate at which the area increases, isAP EAMCET 2005 Hard
- The coordinates of the centre of mass of a uniform L shaped plate of mass 3 kg shown in the figure is
AP EAMCET 2025 Medium - If \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are non coplanar vectors, then the point of intersection of the line passing through the points \(2 \mathbf{a}+3 \mathbf{b}-\mathbf{c}, 3 \mathbf{a}+4 \mathbf{b}-2 \mathbf{c}\) with the line joining the points \(\mathbf{a}-2 \mathbf{b}+3 \mathbf{c}\), \(\mathbf{a}-6 \mathbf{b}+6 \mathbf{c}\) isAP EAMCET 2018 Medium
- intercept of the plane containing the line of intersection of the planes and and also passing through isAP EAMCET 2021 Easy