TS EAMCET · Maths · Indefinite Integration
\(\int \frac{d x}{(x+100) \sqrt{x+99}}=f(x)+c \Rightarrow f(x)\)
- A \(2(x+100)^{1 / 2}\)
- B \(3(x+100)^{1 / 2}\)
- C \(2 \tan ^{-1}(\sqrt{x+99})\)
- D \(2 \tan ^{-1}(\sqrt{x+100})\)
Answer & Solution
Correct Answer
(C) \(2 \tan ^{-1}(\sqrt{x+99})\)
Step-by-step Solution
Detailed explanation
Let \[ \begin{aligned} I & =\int \frac{d x}{(x+100) \sqrt{x+99}} \\ & =\int \frac{d x}{\left.(\sqrt{x+99})^2+1\right) \sqrt{x+99}} \end{aligned} \] Put \(\sqrt{x+99}=t \Rightarrow \frac{1}{\sqrt{x+99}} d x=2 d t\)…
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 \(\frac{2 x^3+x^2-5}{x^4-25}=\frac{A x+B}{x^2-5}+\frac{C x+1}{x^2+5}\), then \((A, B, C)\) equals toTS EAMCET 2014 Medium
- Consider the following differential equations. \[ \begin{aligned} & D_1: y=4 \frac{d y}{d x}+3 x \frac{d x}{d y}: D_2: \frac{d^2 y}{d x^2}=\left(3+\left(\frac{d y}{d x}\right)^2\right)^{\frac{4}{3}} \ & D_3:\left[1+\left(\frac{d y}{d x}\right)\right]^2=\left(\frac{d y}{d x}\right)^2 \end{aligned} \] The ratio of the sum of the orders of \(D_1, D_2\) and \(D_3\) to the sum of their degrees isTS EAMCET 2018 Easy
- If \(f:[1, \infty) \rightarrow[5, \infty)\) is given by \(f(x)=3 x+\frac{2}{x}\), then \(f^{-1}(x)=\)TS EAMCET 2018 Medium
- If \(x-2 y+k=0\) is a tangent to the parabola \(\mathrm{y}^2-4 \mathrm{x}-4 \mathrm{y}+8=0\), then the value of \(\mathrm{K}\) isTS EAMCET 2023 Easy
- If \(f: N \rightarrow Z\) is defined by \[ f(n)=\left\{\begin{array}{l} 2 \text { if } n=3 k, k \in Z \ 10 \text { if } n=3 k+1, k \in Z \ 0 \text { if } n=3 k+2, k \in Z \end{array}\right. \] Then , \(\{n \in N: f(n)>2\}\) is equal toTS EAMCET 2004 Easy
- If \(A\) is an invertible matrix of order \(n\), then the determinant of \(\operatorname{adj} A\) is equal to :TS EAMCET 2006 Medium
More PYQs from TS EAMCET
- If \(\sin ^{-1}\left(\frac{12}{x}\right)+\sin ^{-1}\left(\frac{5}{x}\right)=\frac{\pi}{2}\), then \(x=\)TS EAMCET 2020 Medium
- What is the bond angle in \(\mathrm{ClO}_2\) (OClO)?TS EAMCET 2011 Hard
- A convex lens focusses an object from it on a screen placed away from it. A glass plate (refractive index ) of thickness is inserted between the lens and the screen. What is the distance of the object from the lens, so that its image is again focused on the screen?TS EAMCET 2022 Hard
- A copper disc of radius \(0.1 \mathrm{~m}\) rotates about an axis passing through its centre and perpendicular to its plane with 10 revolutions per second in a uniform transverse magnetic field of \(0.1 \mathrm{~T}\). The emf induced across the radius of the disc isTS EAMCET 2023 Hard
- The displacements of two particles of same mass executing SHM are represented by the equations \(x_1=4 \sin \left(10 t+\frac{\pi}{6}\right) \text { and } x_2=5 \cos (\omega t) .\) The value of \(\omega\) for which the energies of both the particles remain same isTS EAMCET 2010 Medium
- If 3 is a root of \(x^2+k x-24=0\). It is also a root ofTS EAMCET 2002 Easy