TS EAMCET · Maths · Definite Integration
Let \([x]\) be greatest integer function. Then, \(\int_1^1[x+2[x+2[x]]] d x=\)
- A 0
- B -5
- C -7
- D 10
Answer & Solution
Correct Answer
(C) -7
Step-by-step Solution
Detailed explanation
Let \[ \begin{aligned} I & =\int_{-1}^1[x+2[x+2[x]]] d x \\ I & =\int_{-1}^1[x+2[x]+4[x]] d x \\ & {[\because[x+n]=[x]+n] } \\ I & =\int_{-1}^1([x]+2[x]+4[x]) d x \\ I & =\int_{-1}^1 7[x] d x \\ I & =-7 \int_{-1}^0 d x+\int_0^1 o d x \Rightarrow I=-7 \end{aligned} \]
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
- If \(x\) is numerically so small so that \(x^2\) and higher powers of \(x\) can be neglected, then \(\left(1+\frac{2 x}{3}\right)^{3 / 2} \cdot(32+5 x)^{-1 / 5}\) is approximately equal toTS EAMCET 2009 Easy
- \(\int \frac{d x}{\sqrt{\left(5+2 x+x^2\right)^3}}\) is equal toTS EAMCET 2021 Medium
- If the probability distribution of a random variable \(X\) is as follows, then the variance of \(X\) is \begin{array}{|l|c|c|c|c|}\hlineX=x & 2 & 3 & 5 & 9 \\hlineP(X=x) & k & 2 k & 3 k^2 & k^2 \\hline\end{array}TS EAMCET 2024 Easy
- If \(\log 2=a, \log 3=b, \log 7=c\) and \(6^x=7^{x+4}\) then \(x\) is equal toTS EAMCET 2002 Easy
- If an error of is found in the surface area of a sphere when its radius is measured as , then the approximate error that occurs in the volume of the sphere, in cubic centimetres, isTS EAMCET 2022 Easy
- \(\operatorname{Lim}_{n \rightarrow \infty} \frac{\pi}{2 n}\left[\sin \frac{\pi}{2 n}+\sin \frac{2 \pi}{2 n}+\ldots+\sin \frac{\pi}{2}\right]=\)TS EAMCET 2020 Medium
More PYQs from TS EAMCET
- If \(\frac{d}{d x}\left(\frac{2 x+1}{(x+1)^2(x-2)}\right)=\frac{\mathrm{A}}{(x-2)^2}+\frac{\mathrm{B}}{(x+2)^3}+\frac{\mathrm{C}}{(x+1)^2}\) then \(\mathrm{A}+\mathrm{B}+\mathrm{C}=\)TS EAMCET 2022 Easy
- If the distance between \(\mathrm{Na}^{+}\)and \(\mathrm{Cl}^{-}\)ions in sodium chloride crystal is ' \(Y\) ' \(\mathrm{pm}\). The length of the edge of the unit cell will beTS EAMCET 2020 Medium
- Statement (I) : A uniform electric field and a uniform magnetic field are pointed in the same direction. If an electron is projected in the same direction the electron velocity will decrease in magnitude. Statement (II) : Two infinite long parallel wires are carrying current in the same direction. The magnetic field at a point midway between the wires is zero. Statement (III) : No net force acts on a rectangular coil carrying a steady current when suspended in a uniform magnetic field. Which of the following is correct?TS EAMCET 2022 Medium
- The differential equation for which is the general solution, isTS EAMCET 2020 Medium
- If a circle passing through \((1,-2)\) has \(x-y=2\) and \(2 x+\) \(3 y=14\) as its diameters, then the radius of the circle isTS EAMCET 2023 Easy
- \(\int_0^{\frac{\pi}{4}} \frac{\cos ^2 x}{\cos ^2 x+4 \sin ^2 x} d x=\)TS EAMCET 2019 Easy