NCERT Class 12 · Ch 7 Miscellaneous Exercise · Q31
NCERT Class 12 Maths · Chapter 7 Integrals · Miscellaneous Exercise Question 31
Evaluate ∫₁⁴[|x−1|+|x−2|+|x−3|]dx.
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: 19/2.
- Split at x=2 and x=3. On [1,2], [2,3], [3,4] the integrand is respectively 4−x, x, 3x−6.
- The three integrals are 5/2,5/2,9/2; their sum is 19/2.
Master Chapter 7: Integrals
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Integrals.
← Previous Question
Evaluate \(\int\limits_{0}^{\frac{\pi}{2}} \sin{\left(2 x \right)}…
Next Question →Evaluate \(\int\limits_{1}^{3} \frac{1}{x^{2} \left(x + 1\right)}\…
All Questions in Integrals — Miscellaneous Exercise
Related Questions in Integrals
Class 12 Integrals · Mcq Single Correct
Evaluate \(\int x^2e^{x^3}\,dx\).
Class 12 Integrals · Mcq Single Correct
Evaluate \(\int e^x(1+x)\sec^2(xe^x)\,dx\) on an interval where defined.
Class 12 Integrals · Mcq Single Correct
Evaluate \(\int e^x(\cos x-\sin x)\,dx\).
Class 12 Integrals · Mcq Single Correct
Evaluate \(\int dx/(\sin^2x\cos^2x)\) on an interval avoiding its poles.
Class 12 Integrals · Mcq Single Correct
If \(\int\frac{3e^x-5e^{-x}}{4e^x+5e^{-x}}dx=ax+b\ln|4e^x+5e^{-x}|+C\), find a,b.
Class 12 Integrals · Mcq Single Correct
Evaluate \(\int_{-1}^{1}|x-2|/(x-2)\,dx\).