Mathbee CBSE Mathbee · CBSE Class 12 Maths
Class 12 Integrals · Assertion Reason1 Marksintegration_properties

Class 12 Maths · Integrals · Assertion Reason #28

Assertion: \(\int dx/(1+x^2)=\arctan x+C\). Reason: Since \(d(\arctan x)/dx=1/(1+x^2)\), its antiderivative is \(\arctan x+C\).

✅ Step-by-Step Solution

Final Answer: Option (A): Both A and R are true, and R correctly explains A.
  1. The defining derivative–antiderivative relation in R proves A directly.

Master Chapter 7: Integrals

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Integrals.
📘 Chapter Notes & All Exercises 🚀 Open Interactive Workspace →
← Previous Question
Assertion: \(\int_2^8\frac{\sqrt{10-x}}{\sqrt{x}+\sqrt{10-x}}dx=3\)…
Next Question →
Assertion: For x>0, \(\int dx/(2\sqrt{x})=\sqrt{x}+C\). Reason…

More Practice Questions in Integrals

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38Q39Q40

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 \(\int_{-1}^{1}|x-2|/(x-2)\,dx\).