TS EAMCET · Maths · Indefinite Integration
\(\int \frac{d x}{\sqrt{(x-1)(x-2)}}=\)
- A \(\sin ^{-1}(2 x+5)+c\)
- B \(\sinh ^{-1}(2 x-5)+c\)
- C \(\cosh ^{-1}(2 x-3)+c\)
- D \(\sin ^{-1}(3-2 x)+c\)
Answer & Solution
Correct Answer
(C) \(\cosh ^{-1}(2 x-3)+c\)
Step-by-step Solution
Detailed explanation
Let \[ \begin{aligned} I & =\int \frac{d x}{\sqrt{(x-1)(x-2)}}=\int \frac{d x}{\sqrt{x^2-3 x+2}} \\ & =\int \frac{d x}{\sqrt{x^2-2 \cdot \frac{3}{2} \cdot x+\left(\frac{3}{2}\right)^2-\left(\frac{3}{2}\right)^2+2}} \end{aligned} \]…
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 normal at a point on the parabola \(\mathrm{y}^2=4 \mathrm{x}\) passes through \((5,0)\). If there are two more normals to this parabola passing through \((5,0)\), then the equation of one of these normals isTS EAMCET 2023 Medium
- A vessel in the shape of an inverted cone of height \(10 \mathrm{ft}\) and semi vertical angle \(30^{\circ}\) is full of water. Due to a hole at the vertex, the slant height of the water in the vessel is decreasing at a constant rate of \(\frac{1}{\sqrt{3}}\) feet per minute. The rate (in cu. feet \(/ \mathrm{min}\) ) at which the volume of water in the vessel is decreasing, when the volume of water is \(\frac{8 \pi}{\sqrt{3}}\) cubic feet, isTS EAMCET 2020 Medium
- If \(\bar{a}=(x+2 y-3) \bar{i}+(2 x-y+3) \bar{j}\) and \(\bar{b}=(3 x-2 y) \bar{i}+(x-y+1) \bar{j}\) are two vectors such that \(\bar{a}=2 \bar{b}\), then \(y-5 x=\)TS EAMCET 2025 Medium
- If \(f:[a, b] \rightarrow[c, d]\) is a continuous and strictly increasing function, then \(\frac{d-c}{b-a}\) isTS EAMCET 2025 Medium
- \(L_1 \equiv 2 x+y-3=0\) and \(L_2 \equiv a x+b y+c=0\) are two equal sides of an isosceles triangle. If \(L_3 \equiv x+2 y+1=0\) is the third side of this triangle and \((5,1)\) is a point on \(L_2\) \(=0\) then \(\frac{b^2}{|a c|}=\)TS EAMCET 2024 Hard
- If the vector \(\mathbf{a}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}\) and \(\mathbf{b}\) are collinear and \(|\mathbf{b}|=21\), then \(\mathbf{b}\) equal to:TS EAMCET 2005 Easy
More PYQs from TS EAMCET
- Suppose a line makes an angle of \(120^{\circ}\) with the positive direction of \(X\)-axis. If the length of the perpendicular from origin to that line Is 4 , then the equation of the line isTS EAMCET 2019 Easy
- A man walking along a straight line with a velocity \(6 \mathrm{~km} / \mathrm{h}\) encounters rain falling vertically down with a velocity \(6 \sqrt{3} \mathrm{~km} / \mathrm{h}\). At what angle the man should hold his umbrella so that he can protect himself from rainTS EAMCET 2022 Easy
- \(\mathrm{A}(27,-243,81)\) is a point in space. \(\mathrm{B}, \mathrm{C}, \mathrm{D}\) are images of A with respect to \(\mathrm{XY}, \mathrm{YZ}\) and \(\mathrm{ZX}\) planes respectively. If the centroid of the triangle \(\mathrm{BCD}\) is \((\alpha, \beta, \gamma)\), then \(\alpha+\beta+\gamma=\)TS EAMCET 2022 Easy
- Let the centre of the circle \(\mathrm{S}=0\) lie on the line \(x+y-5=0\) and also lie in the first quadrant. If this circle touches both the lines \(x-2=0\) and \(y-5=0\), then the area of the circle isTS EAMCET 2022 Medium
- The sum of the least positive arguments of the distinct cube roots of the complex number \((1-i \sqrt{3})\) isTS EAMCET 2018 Medium
- Which of the following principles is being used in Sonar Technology?TS EAMCET 2017 Easy