Class 12 Integrals · Mcq Single Correct1 Marksintegration
Class 12 Maths · Integrals · Mcq Single Correct #8
Evaluate \(\int\arctan\sqrt{x}\,dx\) for x>0.
✅ Step-by-Step Solution
Final Answer: Option (A): (x+1)arctan√x−√x+C
- Integration by parts gives x arctan√x−(1/2)∫√x/(1+x)dx. Set t=√x; the remainder becomes ∫t²/(1+t²)dt=t−arctan t, giving option a.
Master Chapter 7: Integrals
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Integrals.
← Previous Question
For real a,b with \(\sin(b-a)\ne0\), evaluate \(\int…
Next Question →Evaluate \(\int e^x[(1-x)/(1+x^2)]^2\,dx\).
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 \(\int_{-1}^{1}|x-2|/(x-2)\,dx\).