TS EAMCET · Maths · Definite Integration
If \(f\) is defined on \(\mathbb{R}\) such that \(f(\mathrm{x}) f(-\mathrm{x})=9\), then \(\int_{-23}^{23} \frac{d x}{3+f(x)}\)
- A \(\frac {51}{3}\)
- B \(\frac {49}{3}\)
- C \(\frac {46}{3}\)
- D \(\frac {46}{6}\)
Answer & Solution
Correct Answer
(D) \(\frac {46}{6}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & f(x) \cdot f(-x)=9 \\ & I=\int_{-23}^{23} \frac{d x}{3+f(x)}... (i) \\ & I=\int_{-23}^{23} \frac{d x}{3+f(-x)} \quad(f(a+b-x) \text { property }) \\ & I=\int_{-23}^{23} \frac{d x}{3+\frac{9}{f(x)}}=\int_{-23}^{23} \frac{f(x) d x}{3(f(x)+3)}... (ii) \\ & \text {…
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
- Let be the unique solution of the system of simultaneous linear equations . If thenTS EAMCET 2022 Medium
- The real part of \(z\) that satisfies \(i z^4+1=0\) isTS EAMCET 2019 Medium
- The radius of a cone of height 9 units is changed from 2 units to 2.12 units. The exact change and approximate change in the volume of the cone are respectivelyTS EAMCET 2025 Medium
- The random variable takes the values \(1,2,3\), \(\ldots, m\). If \(P(X=n)=\frac{1}{m}\) to each \(n\), then the variance of \(X\) isTS EAMCET 2013 Hard
- If \(m_1\) and \(m_2\) are the slopes of the direct common tangents drawn to the circles \(x^2+y^2-2 x-8 y+8=0\) and \(x^2+y^2-8 x+15=0\), then \(m_1+m_2=\)TS EAMCET 2024 Hard
- TS EAMCET 2021 Easy
More PYQs from TS EAMCET
- \(\lim _{x \rightarrow 0} \frac{\left(2^x-1\right)(1+\sin x)^{\frac{2}{\sin x}}}{\log (1+2 x)}=\)TS EAMCET 2022 Medium
- If \(\frac{3 \mathrm{x}+2}{(\mathrm{x}+1)\left(2 \mathrm{x}^2+3\right)}=\frac{\mathrm{A}}{\mathrm{x}+1}+\frac{\mathrm{Bx}+\mathrm{C}}{2 \mathrm{x}^2+3}\), then \(\mathrm{A}-\mathrm{B}+\mathrm{C}=\)TS EAMCET 2023 Medium
- If \(\theta\) is the acute angle between the pair of lines \(12 x^2+2 h x y+7 y^2=0\) and \(\tan \theta=\frac{8}{19}\), then \(h=\)TS EAMCET 2022 Easy
- In environmental chemistry, the medium which is affected by a pollutant is called as theTS EAMCET 2016 Easy
- If is the point to which the origin is to be shifted by translation of axes so as to remove the first degree terms from the equation and is the angle through which the axes are to be rotated about the origin so as to remove the -term from the above equation, thenTS EAMCET 2021 Hard
- A solid sphere of radius makes a perfect rolling down on a plane which is inclined to the horizontal axis at an angle . If the radius of gyration is , then its acceleration isTS EAMCET 2018 Hard