Integrals are central to Class 12 Mathematics because they connect area/accumulation with powerful tools like substitution, symmetry, partial fractions, and parameter-based techniques. Mastering standard integral results and proving them using differentiation under the integral sign or series expansions is crucial for board exams and is also a strong base for competitive exams like JEE/NEET, where unseen integrals often reduce to these core patterns.
25
Minutes
20
Questions
1 / -0
Marking
Q1. Evaluate the integral .
Q2. Let . The value of is
Q3. Evaluate .
Q4. Consider the statements: A: The improper integral converges. R: The function is absolutely integrable on .
Both A and R are true and R is a correct explanation of A.
Both A and R are true but R is not a correct explanation of A.
A is true but R is false.
A is false but R is true.
Q5. Let . Evaluate .
Q6. Evaluate the definite integral .
Q7. Evaluate .
Q8. Evaluate .
Q9. Assertion (A): For , .
Reason (R): Differentiating with respect to under the integral sign gives , and integrating this identity with respect to (using the value at ) yields .
Both A and R are true but R is not the correct explanation of A.
A is false but R is true.
Both A and R are false.
Both A and R are true and R is the correct explanation of A.
Q10. Evaluate the improper integral .
Q11. Evaluate the definite integral .
Q12. Evaluate the integral .
Q13. For integer , evaluate .
Q14. Evaluate the integral .
Q15. For , evaluate .
...and 5 more challenging questions available in the interactive simulator.