TS 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
\(\int_0^3 \frac{3 x+1}{x^2+9} d x=\frac{3}{2} \int_0^3 \frac{2 x}{x^2+9} d x+\int_0^3 \frac{1}{x^2+9} d x\) \(=\frac{3}{2}\left[\log \left(x^2+9\right)\right]_0^3+\frac{1}{3}\left[\tan ^{-1} \frac{x}{3}\right]_0^3\)…
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
- Two circles of equal radius \(a\) cut orthogonally. If their centres are \((2,3)\) and \([5,6]\) then radical axis of these circles passes through the pointTS EAMCET 2017 Medium
- If thenTS EAMCET 2021 Easy
- If thenTS EAMCET 2021 Medium
- If the points with position vectors \(60 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}, 40 \hat{\mathbf{i}}-8 \hat{\mathbf{j}}\) and \(a \hat{\mathbf{i}}-52 \hat{\mathbf{j}}\) are collinear, then \(a\) is equal toTS EAMCET 2008 Easy
- The value of the numerically greatest term in the expansion of when and isTS EAMCET 2021 Easy
- In a triangle, if the length of the sides and are three consecutive natural numbers and thenTS EAMCET 2021 Easy
More PYQs from TS EAMCET
- The equation of a straight line passing through the point \((1,2)\) and inclined at \(45^{\circ}\) to the line \(y=2 x+1\) isTS EAMCET 2012 Medium
- \(\log (9+3 \sqrt{2}(2+\sqrt{5})+4 \sqrt{5})=\)TS EAMCET 2020 Medium
- If the vectors \(\mathbf{A B}=p \hat{\mathbf{i}}+q \hat{\mathbf{j}}+r \hat{\mathbf{k}}\), \(\mathbf{A C}=s \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, \mathbf{C B}=3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}\) from \(\triangle A B C\), then the values of \(p, q, r\) and \(s\) such that the area of that \(\triangle A B C\) is \(5 \sqrt{6}\) areTS EAMCET 2020 Hard
- Maximum number of bromine atoms present in the final product \(P\) upon complete bromination are
TS EAMCET 2020 Hard - Neoprene is the polymer of a monomer X. IUPAC name of X isTS EAMCET 2025 Easy
- If the line \(y=-4 x+b\) is tangent to the curve \(y=\frac{1}{x}\), then \(b\) equalsTS EAMCET 2015 Easy