Class 12 Integrals · Short Answer2 Marksdefinite_integration
Class 12 Maths · Integrals · Short Answer #55
Evaluate \(\int_0^1\arctan x/(1+x^2)dx\).
✅ Step-by-Step Solution
Final Answer: π²/32
- Set u=arctan x, du=dx/(1+x²), with limits 0 and π/4.
- The integral becomes ∫₀^(π/4)u du=[u²/2]₀^(π/4)=π²/32.
- Therefore the integral equals π²/32.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Set u=arctan x, du=dx/(1+x²), with limits 0 and π/4.
- [1 mark] The integral becomes ∫₀^(π/4)u du=[u²/2]₀^(π/4)=π²/32.
- [0.5 marks] Therefore the integral equals π²/32.
Master Chapter 7: Integrals
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Integrals.
← Previous Question
Evaluate \(\int e^x\sqrt{1+\sin2x}/(1+\cos2x)\,dx\) on intervals…
Next Question →Evaluate \(\int_0^1 dx/\sqrt{2x+3}\).
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 \(\int_{-1}^{1}|x-2|/(x-2)\,dx\).