Chapter Exam

Unit 6: Integration — Online MCQ Test

Q: The integral of sec^2(x) dx is equal to:

Answer: A. tan(x) + c — By the standard formula of integration, the antiderivative of sec^2(x) is tan(x) plus the constant of integration.

Q: Which of the following represents the integral of 1/x dx?

Answer: B. log|x| + c — The standard integral of 1/x is defined as the natural logarithm of the absolute value of x plus a constant.

Q: Evaluate ∫ 2x dx.

Answer: A. x^2 + c — Using the power rule ∫ x^n dx = x^(n+1)/(n+1), for n=1, we get x^2/2, multiplied by 2 gives x^2.

Q: Evaluate ∫ tan(x) dx:

Q: Find ∫ (sin x / (sin x + cos x)) dx, given it is a special integral form:

Answer: A. x/2 - 1/2 log|sin x + cos x| + c — By expressing the numerator as A(den) + B(d/dx den), one obtains 1/2 ∫(1 dx) - 1/2 ∫((cos x - sin x)/(sin x + cos x)) dx.

MATHEMATICS - 2B · CLASS 12 INTERMEDIATE 2 YEAR · Telangana State Board

Practice Unit 6: Integration with a free chapter-wise online MCQ test for Telangana State Board CLASS 12 INTERMEDIATE 2 YEAR MATHEMATICS - 2B. This chapter covers: Focusing on indefinite calculus this chapter details standard integration formulas integration by substitution integration by parts partial fractions decomposition and reduction fo.... 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.

Unit 6: Integration — Important Questions & Answers (FAQ)

Frequently asked questions from Telangana State Board CLASS 12 INTERMEDIATE 2 YEAR MATHEMATICS - 2B — Unit 6: Integration, with answers and explanations. These are sample questions; the exam has its own separate question set.

The integral of sec^2(x) dx is equal to:

A. tan(x) + c ✓
B. sec(x) + c
C. cos^2(x) + c
D. tan(x)sec(x) + c

Answer: A. tan(x) + c
By the standard formula of integration, the antiderivative of sec^2(x) is tan(x) plus the constant of integration.

Which of the following represents the integral of 1/x dx?

A. x^2/2 + c
B. log|x| + c ✓
C. e^x + c
D. 1 + c

Answer: B. log|x| + c
The standard integral of 1/x is defined as the natural logarithm of the absolute value of x plus a constant.

Evaluate ∫ 2x dx.

A. x^2 + c ✓
B. 2x^2 + c
C. x + c
D. 2 + c

Answer: A. x^2 + c
Using the power rule ∫ x^n dx = x^(n+1)/(n+1), for n=1, we get x^2/2, multiplied by 2 gives x^2.

Evaluate ∫ tan(x) dx:

A. sec^2(x) + c
B. log|sec(x)| + c
C. -log|cos(x)| + c
D. Both B and C are correct ✓

Find ∫ (sin x / (sin x + cos x)) dx, given it is a special integral form:

A. x/2 - 1/2 log|sin x + cos x| + c ✓
B. x/2 + 1/2 log|sin x + cos x| + c
C. log|sin x + cos x| + c
D. 1/2 (x - log|cos x - sin x|) + c

Answer: A. x/2 - 1/2 log|sin x + cos x| + c
By expressing the numerator as A(den) + B(d/dx den), one obtains 1/2 ∫(1 dx) - 1/2 ∫((cos x - sin x)/(sin x + cos x)) dx.