Unit 6: Integration — Online MCQ Test
MATHEMATICS - 2B · CLASS 12 INTERMEDIATE 2 YEAR · Telangana State Board
Practice Unit 6: Integration with a free chapter-wise online MCQ test.
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....
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Unit 6: Integration — Important Questions & Answers
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.
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.
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.
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
Answer: D. Both B and C are correct
Since log|sec(x)| = log|1/cos(x)| = -log|cos(x)|, both representations are valid equivalents.
Since log|sec(x)| = log|1/cos(x)| = -log|cos(x)|, both representations are valid equivalents.
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.
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.