AP EAMCET · Maths · Definite Integration
\(\int_0^3 \frac{3 x+1}{x^2+9} d x\) is equal to :
- A \(\log (2 \sqrt{2})+\frac{\pi}{12}\)
- B \(\log (2 \sqrt{2})+\frac{\pi}{2}\)
- C \(\log (2 \sqrt{2})+\frac{\pi}{6}\)
- D \(\log \left(2(\sqrt{2})+\frac{\pi}{3}\right.\)
Answer & Solution
Correct Answer
(A) \(\log (2 \sqrt{2})+\frac{\pi}{12}\)
Step-by-step Solution
Detailed explanation
\(=\frac{3}{2}\left[\log \left(x^2+9\right)\right]_0^3+\frac{1}{3}\left[\tan ^{-1} \frac{x}{3}\right]_0^3\) \(=\frac{3}{2}[\log 18-\log 9]+\frac{1}{3}\left[\tan ^{-1}(1)-\tan ^{-1}(0)\right]\) \(=\frac{3}{2}[\log 2]+\frac{\pi}{12}\) \(=\log (2 \sqrt{2})+\frac{\pi}{12}\)
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 number of ways of forming the ordered pairs ( \(p, q\) ) such that \(p>q\) by choosing p and q from the first 50 natural numbers isAP EAMCET 2025 Medium
- In a \(\triangle A B C\), if \(a \cos A=b \cos B\), where \(a \neq b\), then \(\triangle A B C\) isAP EAMCET 2022 Medium
- The general solution of \(\left(1+e^{\frac{x}{y}}\right) d x+e^{\frac{x}{y}}\left(1-\frac{x}{y}\right) d y=0\) isAP EAMCET 2018 Easy
- If \(e_1\) and \(e_2\) are the eccentricities of the hyperbola \(16 x^2-9 y^2=1\) and its conjugate respectively. Then, \(3 e_1=\)AP EAMCET 2022 Medium
- If the lines represented by the equation are real then the value of ' ' lies in the intervalAP EAMCET 2021 Easy
- If \(x-2=t^2, y=2 t\) are the parametric equations of the parabola \(y^2=a(x-b)\), then the value of \(a+b\) equalsAP EAMCET 2021 Easy
More PYQs from AP EAMCET
- Let the tangents drawn from \(\mathrm{P}(-1,-1)\) to the circle \(x^2+y^2-2 x-4 y-4=0\) touch the circle at the points \(\mathrm{A}\) and \(\mathrm{B}\). Then the area of the triangle \(\mathrm{PAB}\) (in square units) isAP EAMCET 2017 Medium
- At \(\mathrm{T}(\mathrm{K})\), the vapour pressures of two liquids, heptane and octane are \(106 \mathrm{kPa}\) and \(47 \mathrm{kPa}\) respectively. If \(25 \mathrm{~g}\) of heptane and \(57 \mathrm{~g}\) of octane form an ideal solution, at \(\mathrm{T}(\mathrm{K})\) the vapour pressure of solution in \(\mathrm{kPa}\) is :AP EAMCET 2017 Medium
- If the point of intersection of the pair of the transverse common tangents and that of the pair of direct common tangents drawn to the circles \(x^2+y^2-14 x+6 y+33=0\) and \(x^2+y^2+30 x-2 y+1=0\) are \(T\) and \(D\) respectively, then the centre of the circle having TD as diameter isAP EAMCET 2019 Hard
- In any triangle \(\mathrm{ABC}, \sin \frac{A}{2} \leq\)AP EAMCET 2022 Medium
- A prism of refractive index \(\mu\) and angle \(A\) is placed in the minimum deviation position. If the angle of minimum deviation is \(A\), then the value of \(A\) in terms of \(\mu\) is :AP EAMCET 2003 Hard
- The system of two masses \(2 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) as shown in the figure is released from rest. The work done on \(3 \mathrm{~kg}\) block by the force of gravity during first 2 seconds of its motion is \(\left(g=10 \mathrm{~ms}^{-2}\right)\)
AP EAMCET 2018 Medium