Class 12 Integrals · Long Answer3 Marksdefinite_integration
Class 12 Maths · Integrals · Long Answer #104
Evaluate \(\int_{-2}^2x^2/(1+5^x)dx\).
✅ Step-by-Step Solution
Final Answer: 8/3
- Let I be the integral. Reflect x↦−x; x² is unchanged.
- The reflected expression is I=∫₋₂²5^x x²/(1+5^x)dx.
- Add the two expressions to get 2I=∫₋₂²x²dx=16/3.
- Therefore the integral equals 8/3.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Let I be the integral. Reflect x↦−x; x² is unchanged.
- [1 mark] The reflected expression is I=∫₋₂²5^x x²/(1+5^x)dx.
- [1 mark] Add the two expressions to get 2I=∫₋₂²x²dx=16/3.
- [0.5 marks] Therefore the integral equals 8/3.
Master Chapter 7: Integrals
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Integrals.
← Previous Question
Evaluate \(\int_0^\pi e^{2x}\sin(x+\pi/4)dx\).
Next Question →Evaluate \(\int_0^\pi x\tan x/(\sec x+\tan x)dx\), using the…
More Practice Questions in Integrals
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 \(\int_{-1}^{1}|x-2|/(x-2)\,dx\).