Chapter 11: Integral Calculus — Online MCQ Test
MATHS · CLASS 11th · Tamil Nadu State Board
Practice Chapter 11: Integral Calculus with a free chapter-wise online MCQ test.
This chapter covers: This chapter introduces indefinite integration basic rules integration techniques and simple integral applications. Students master substitution integration by parts and trigonomet....
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Chapter 11: Integral Calculus — Important Questions & Answers
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.
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.
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.
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.
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.
Using the standard formula ∫dx/(x^2 + a^2) = (1/a)tan^-1(x/a) + C with a = 3 gives the answer.