AP EAMCET · Maths · Definite Integration
\(\int_0^3\left|x^2-3 x+2\right| d x=\)
- A \(\frac{3}{2}\)
- B \(\frac{1}{6}\)
- C \(\frac{11}{6}\)
- D \(\frac{11}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{11}{6}\)
Step-by-step Solution
Detailed explanation
Let \(I=\int_0^3\left|x^2-3 x+2\right| d x\) \(\because \quad x^2-3 x+2=(x-2)(x-1)\) So, \(\quad x^2-3 x+2 < 0\) for \(x \in(1,2)\) and \(x^2-3 x+2 \geq 0\) for \(x \in R-(1,2)\) So,…
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 and are two vectors such that and and are perpendicular, where is a positive scalar, thenAP EAMCET 2021 Easy
- The triangle \(P Q R\) is inscribed in the circle \(x^2+y^2=25\). If \(\mathrm{Q}=(3,4)\) and \(\mathrm{R}=(-4,3)\) then \(\angle \mathrm{QPR}=\)AP EAMCET 2024 Easy
- If a point \(P\) on the line \(3 x+5 y=15\) is equidistant from the coordinate axes, then \(P\) liesAP EAMCET 2021 Easy
- If \(f: R \rightarrow R\) defined by
\[
f(x)=\left\{\begin{array}{cc}
a^2 \cos ^2 x+b^2 \sin ^2 x, & x \leq 0 \\
e^{a x+b}, & x>0
\end{array}\right.
\]
is a continuous function, thenAP EAMCET 2002 Hard - Assertion (A):If \(\mathrm{A}=10^{\circ}, \mathrm{B}=16^{\circ}, \mathrm{C}=19^{\circ}\), then \(\tan 2 \mathrm{~A}\) \(\tan 2 \mathrm{~B}+\tan 2 \mathrm{~B} \tan 2 \mathrm{C}+\tan 2 \mathrm{C} \tan 2 \mathrm{~A}=1\).
Reason (R): If \(A+B+C=180^{\circ},=\cot \frac{A}{2} \cdot \cot \frac{B}{2} \cdot \cot \frac{C}{2}\) \(=\cot \frac{\mathrm{A}}{2} \cdot \cot \frac{\mathrm{~B}}{2} \cdot \cot \frac{\mathrm{C}}{2}\)
Which of the following is correct?AP EAMCET 2024 Medium - The general solution of the differential equation \(\frac{d y}{d x}+\frac{x+y+1}{x-3 y+5}=0\) isAP EAMCET 2025 Medium
More PYQs from AP EAMCET
- An electron accelerated through a potential difference \(V\), passes through a uniform transverse magnetic field and experiences a force \(F\). If the accelerating potential is increased to \(2 \mathrm{~V}\), the electron in the same magnetic field will experience a force.AP EAMCET 2019 Medium
- The energy of \(E\) of a system is function of time \(t\) and is given by \(E(t)=\alpha t-\beta t^3\), where \(\alpha\) and \(\beta\) are constants. The dimensions of \(\alpha\) and \(\beta\) areAP EAMCET 2022 Easy
- Let \(\mathbf{a}=\mathbf{i}+2 \mathbf{j}+\mathbf{k}, \mathbf{b}=\mathbf{i}-\mathbf{j}+\mathbf{k}, \mathbf{c}=\mathbf{i}+\mathbf{j}-\mathbf{k}\). A vector in the plane of \(\mathbf{a}\) and \(\mathbf{b}\) has projection \(\frac{1}{\sqrt{3}}\) on c. Then, one such vector isAP EAMCET 2012 Easy
- Nitrous acid was disproportionated to form water, \(\mathrm{HNO}_3\) and \(X\). In another reaction, sodium nitrite was reacted with \(\mathrm{H}_2 \mathrm{SO}_4\) to form \(\mathrm{NaHSO}_4, \mathrm{HNO}_3\), water and \(Y\). What are \(X\) and \(Y\) respectively?AP EAMCET 2018 Medium
- If \(\int \frac{5 \cot x+1}{(\cot x-1)(\cot x-2) \sin ^2 x} d x\)
\(=6 \log |f(x)|+11 \log |g(x)|+c\), then \((f(x), g(x))=\)AP EAMCET 2019 Medium - \(\frac{\tan 80^{\circ}-\tan 10^{\circ}}{\tan 70^{\circ}}\) is equal toAP EAMCET 2007 Medium