AP EAMCET · Maths · Definite Integration
\(\int_{-1}^2|x| d x=\)
- A 1
- B 2
- C \(\frac{5}{2}\)
- D \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{5}{2}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} I & =\int_{-1}^2|x| d x=\int_{-1}^0(-x) d x+\int_0^2(x) d x \\ & =\left[\frac{-x^2}{2}\right]_{-1}^0+\left[\frac{x^2}{2}\right]_0^2=\left(0+\frac{1}{2}\right)+\left(\frac{4}{2}-0\right)=\frac{5}{2} \end{aligned}\)
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
- \[
\int \frac{\cos ^4 x}{\left(\sin ^2 x+\sin ^{-3} x \cos ^5 x\right)^3} d x=
\]AP EAMCET 2022 Medium - For the circle \(C\) with the equation \(x^2+y^2-16 x-12 y+64=0\) match the List I with the List II given below.
The correct match is
\(\begin{array}{llll}(\mathrm{i}) & (\mathrm{ii}) & (\mathrm{iii}) & (\mathrm{iv})\end{array}\)AP EAMCET 2013 Medium - Let \(\mathrm{A}\) and \(\mathrm{B}\) be two independent events of a random experiment. If the probability that both A and B occur is \(\frac{1}{6}\) and the probability that neither of them occur is \(\frac{1}{3}\), then the probability of occurrence of \(\mathrm{A}\) isAP EAMCET 2023 Hard
- If \(\int \sin ^5 x d x=\frac{-\cos ^5 x}{5}+a \cos ^3 x+b \cos x+c\), then \(a+b=\)AP EAMCET 2017 Medium
- Variance of the following discrete frequency distribution is
Class Interval 0–2 2–4 4–6 6–8 8–10 Frequency 2 3 5 3 2 AP EAMCET 2025 Medium - The absolute value of the tangent of the difference of the angles made by the lines \(4 x^2-24 x y+11 y^2=0\) with the \(\mathrm{X}\)-axis isAP EAMCET 2023 Medium
More PYQs from AP EAMCET
- Ag crystallises in fcc lattice. What is the total number of tetrahedral voids present in \(540 \mathrm{~g}\) of Ag metal? \(\left(N_A=\right.\) Avagadro number; \(\mathrm{Ag}\) atomic weight \(=108 \mathrm{~g} \mathrm{~mol}^{-1}\) )AP EAMCET 2022 Medium
- \(\lim _{x \rightarrow \infty} \frac{1^{77}+2^{77}+\ldots+n^{77}}{n^{78}}=\)AP EAMCET 2024 Easy
- The number of oxygen atoms bonded to one phosphorous atom in \(\mathrm{P}_4 \mathrm{O}_6\) isAP EAMCET 2004 Medium
- Which of the following statements is true?
(i) The two axial \(\mathrm{P}-\mathrm{Cl}\) bonds in \(\mathrm{PCl}_5\) are longer than the three equatorial bonds.
(ii) The axial bonds in \(\mathrm{PCl}_5\) are stronger than equatorial bonds.
(iii) The axial bonds in \(\mathrm{PCl}_5\) are more stable than equatorial bonds.
(iv) All five bonds in \(\mathrm{PCl}_5\) molecule are equivalent.AP EAMCET 2020 Medium - The position of a particle at time \(t\) is given by the equation \(x(t)=\frac{v_0}{A}\left(1-e^{A t}\right) v_o=\) constant and \(A>0\). Dimensions of \(v_o\) and A respectively areAP EAMCET 2004 Easy
- The ratio between RMS velocities of \(\mathrm{H}_2\) at \(50 \mathrm{~K}\) and \(\mathrm{O}_2\) at \(800 \mathrm{~K}\) isAP EAMCET 2019 Easy