NCERT Class 12 · Ch 7 Exercise 7.10 · Q5
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.10 Question 5
Evaluate \(\int\limits_{-5}^{5} \left|{x + 2}\right|\, dx\) using definite-integral properties.
💡 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: \(29\)
- Split the interval at x=-2, where the expression inside the absolute value changes sign.
- Integrate the negative linear branch to the left and positive linear branch to the right, or add their triangular areas. The sum is \(29\).
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}} \frac{\cos^{5}{\left(x…
Next Question →Evaluate \(\int\limits_{2}^{8} \left|{x - 5}\right|\, dx\) using…
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 \(\int_{-1}^{1}|x-2|/(x-2)\,dx\).