MHT CET · Maths · Definite Integration
\(\int_0^4|2 x-5| \mathrm{d} x=\)
- A \(\frac{13}{2}\)
- B \(\frac{15}{2}\)
- C \(\frac{17}{4}\)
- D \(\frac{17}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{17}{2}\)
Step-by-step Solution
Detailed explanation
\(\int_0^4|2 x-5| \mathrm{d} x =\int_0^{\frac{5}{2}}(5-2 x) \mathrm{d} x+\int_{\frac{5}{2}}^4(2 x-5) \mathrm{d} x \)
\( =\left[5 x-x^2\right]_0^{\frac{5}{2}}+\left[x^2-5 x\right]_{\frac{5}{2}}^4 \)
\( =\frac{25}{4}+\frac{9}{4} \)
\( =\frac{34}{4} \)
\( =\frac{17}{2}\)
\( =\left[5 x-x^2\right]_0^{\frac{5}{2}}+\left[x^2-5 x\right]_{\frac{5}{2}}^4 \)
\( =\frac{25}{4}+\frac{9}{4} \)
\( =\frac{34}{4} \)
\( =\frac{17}{2}\)
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
- \(f(x) \begin{cases}=\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x} & \text {, if } 1 \leq x < 0 \ =\frac{2 x+1}{x-2} \end{cases}\) \(\text {, if } 0 \leq x \leq 1\)
is continuous in the interval \([-1,1]\), then \(\mathrm{p}=\)MHT CET 2021 Easy - If \(x \frac{\mathrm{~d} y}{\mathrm{~d} x}=y(\log y-\log x+1)\), then general solution of this equation isMHT CET 2024 Medium
- If \(\left(\frac{1-i}{1+i}\right)^{100}=a+i b\), where, \(a b \in R\) and \(i=\sqrt{-1}\), then \((a, b)\) is equal toMHT CET 2022 Easy
- If \(y=\log \tan \left(\frac{x}{2}\right)+\sin ^1(\cos x)\), then \(\frac{d y}{d x}=\)MHT CET 2021 Medium
- \(\tan ^{-1}\left(\tan \frac{5 \pi}{6}\right)+\cos ^{-1}\left(\cos \frac{13 \pi}{6}\right)=\)MHT CET 2021 Easy
- If \(A=\left[\begin{array}{cc}2 & -1 \\ -1 & 2\end{array}\right]\) such that \(A^2-4 A+3 I=0\), where \(\mathrm{I}\) is a unit matrix of order 2 , then \(A^{-1}\) isMHT CET 2022 Medium
More PYQs from MHT CET
- Chromyl chloride converts methyl group to a chromium complex, which on acid hydrolysis gives corresponding aldehyde. This reaction is calledMHT CET 2020 Easy
- \(\int e^{\tan x}\left(\sec ^2 x+\sec ^3 x \sin x\right) d x=\)MHT CET 2021 Medium
- The value of \(\int \frac{2 x^{12}+5 x^9}{\left(x^5+x^3+1\right)^3} \mathrm{~d} x\) is equal to (where \(C\) is arbitrary constant.)MHT CET 2022 Easy
- If the vectors \(\overline{\mathrm{a}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overline{\mathrm{b}}=2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+\hat{\mathrm{k}}\) and \(\overline{\mathrm{c}}=\lambda \hat{\mathrm{i}}+\hat{\mathrm{j}}+\mu \hat{\mathrm{k}}\) are mutually orthogonal, then \((\lambda, \mu) \equiv\)MHT CET 2024 Easy
- A block of mass M is pulled along a smooth horizontal surface with a rope of mass m by force F. The acceleration of the block will beMHT CET 2019 Easy
- \({}_{90}\mathrm{Th}^{232} \)\(\longrightarrow{ }_{82} \mathrm{~Pb}^{208}\). The number of \(\alpha\) and \(\beta\) -particles emitted during the above reaction isMHT CET 2007 Hard