Chapter Exam

Chapter 11: Integral Calculus — Online MCQ Test

Q: What is the integral of x^n with respect to x, where n ≠ -1?

Answer: A. x^(n+1)/(n+1) + C — By the power rule of integration, ∫x^n dx = x^(n+1)/(n+1) + C for n ≠ -1.

Q: Which of the following is an indefinite integral of cos x?

Answer: B. sin x + C — Since d/dx(sin x) = cos x, the integral of cos x is sin x + C.

Q: Evaluate ∫(2x) / (x^2 + 1) dx.

Answer: A. ln(x^2 + 1) + C — Using substitution u = x^2 + 1, du = 2x dx, the integral becomes ∫du/u = ln|u| + C = ln(x^2 + 1) + C.

Q: Evaluate ∫x/(x^2 + 4) dx.

Answer: A. (1/2)ln(x^2 + 4) + C — Let u = x^2 + 4, then du = 2x dx. So the integral becomes (1/2)∫du/u = (1/2)ln(x^2 + 4) + C.

Q: Evaluate ∫dx / (x^2 + 9).

Answer: A. (1/3)tan^-1(x/3) + C — Using the standard formula ∫dx/(x^2 + a^2) = (1/a)tan^-1(x/a) + C with a = 3 gives the answer.

MATHS · CLASS 11th · Tamil Nadu State Board

Practice Chapter 11: Integral Calculus with a free chapter-wise online MCQ test for Tamil Nadu State Board CLASS 11th MATHS. This chapter covers: This chapter introduces indefinite integration basic rules integration techniques and simple integral applications. Students master substitution integration by parts and trigonomet.... AI-generated questions from basic to board-exam level, with instant results and explanations.

Questions

20m

Time Limit

Attempts Left

10 random questions from this chapter (mixed difficulty)
Questions you've seen before won't repeat until the pool resets
You have 20 minutes — exam auto-submits when time is up
Maximum 3 attempts per chapter
Results and explanations shown immediately after submission

New here? Register free — includes 3 free chapter exams.

Chapter 11: Integral Calculus — Important Questions & Answers (FAQ)

Frequently asked questions from Tamil Nadu State Board CLASS 11th MATHS — Chapter 11: Integral Calculus, with answers and explanations. These are sample questions; the exam has its own separate question set.

What is the integral of x^n with respect to x, where n ≠ -1?

A. x^(n+1)/(n+1) + C ✓
B. n*x^(n-1) + C
C. ln x + C
D. 1/(n+1)x^n + C

Answer: A. x^(n+1)/(n+1) + C
By the power rule of integration, ∫x^n dx = x^(n+1)/(n+1) + C for n ≠ -1.

Which of the following is an indefinite integral of cos x?

A. -sin x + C
B. sin x + C ✓
C. -cos x + C
D. tan x + C

Answer: B. sin x + C
Since d/dx(sin x) = cos x, the integral of cos x is sin x + C.

Evaluate ∫(2x) / (x^2 + 1) dx.

A. ln(x^2 + 1) + C ✓
B. 1/(x^2 + 1) + C
C. 2ln(x^2 + 1) + C
D. arctan x + C

Answer: A. ln(x^2 + 1) + C
Using substitution u = x^2 + 1, du = 2x dx, the integral becomes ∫du/u = ln|u| + C = ln(x^2 + 1) + C.

Evaluate ∫x/(x^2 + 4) dx.

A. (1/2)ln(x^2 + 4) + C ✓
B. ln(x^2 + 4) + C
C. (1/4)ln(x^2 + 4) + C
D. 2ln(x^2 + 4) + C

Answer: A. (1/2)ln(x^2 + 4) + C
Let u = x^2 + 4, then du = 2x dx. So the integral becomes (1/2)∫du/u = (1/2)ln(x^2 + 4) + C.

Evaluate ∫dx / (x^2 + 9).

A. (1/3)tan^-1(x/3) + C ✓
B. 3tan^-1(x/3) + C
C. tan^-1(3x) + C
D. (1/9)tan^-1(x/3) + C

Answer: A. (1/3)tan^-1(x/3) + C
Using the standard formula ∫dx/(x^2 + a^2) = (1/a)tan^-1(x/a) + C with a = 3 gives the answer.

Choose Your Plan & Start Practising

All plans cover every subject and chapter of your registered grade.

Free

₹0

3 exams · 1 year

Start Free →

Active

₹350

12 exams · 1 year

Get Active →

Pro

₹899

Unlimited exams · 1 year

Get Pro →

Compare all plans in detail →