Chapter 7: Integrals — Online MCQ Test
MATHS · Grade 12 · CBSE(NCERT)
Practice Chapter 7: Integrals with a free chapter-wise online MCQ test.
This chapter covers: Inverse Process: Integration acts as the exact reverse process of differentiation, earning it the alternative name "anti-derivative."Indefinite Integrals: Indefinite integration ma....
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Chapter 7: Integrals — Important Questions & Answers
Integration is the reverse process of which mathematical operation?
- A. Differentiation
- B. Multiplication
- C. Division
- D. Exponentiation
Answer: A. Differentiation
Integration is defined as the inverse or anti-derivative process of differentiation, making it the exact reverse operation.
Integration is defined as the inverse or anti-derivative process of differentiation, making it the exact reverse operation.
What is the arbitrary constant added to an indefinite integral called?
- A. Integration factor
- B. Constant of integration
- C. Differential constant
- D. Limit constant
Answer: B. Constant of integration
The arbitrary constant C added to indefinite integrals accounts for the family of curves differing by a constant.
The arbitrary constant C added to indefinite integrals accounts for the family of curves differing by a constant.
What is the fundamental difference between definite and indefinite integrals?
- A. Indefinite integrals have limits; definite integrals do not
- B. Definite integrals have limits and produce a scalar value; indefinite integrals do not have limits and include C
- C. Both are identical in form and calculation
- D. Definite integrals are always larger than indefinite integrals
Answer: B. Definite integrals have limits and produce a scalar value; indefinite integrals do not have limits and include C
Definite integrals ∫ₐᵇ f(x)dx have numerical limits and result in a specific value, while indefinite integrals produce a family of functions with constant C.
Definite integrals ∫ₐᵇ f(x)dx have numerical limits and result in a specific value, while indefinite integrals produce a family of functions with constant C.
Using integration by substitution, ∫ sin(2x) dx = ?
- A. -cos(2x)/2 + C
- B. -cos(2x) + C
- C. cos(2x)/2 + C
- D. 2cos(2x) + C
Answer: A. -cos(2x)/2 + C
Let u = 2x, du = 2dx. Then ∫ sin(2x) dx = (1/2)∫ sin(u) du = -cos(u)/2 + C = -cos(2x)/2 + C.
Let u = 2x, du = 2dx. Then ∫ sin(2x) dx = (1/2)∫ sin(u) du = -cos(u)/2 + C = -cos(2x)/2 + C.
Consider ∫ (3x+5)/(x²+4x+8) dx. After completing the square in denominator and substitution, this becomes:
- A. An integral of form ∫ (du/u) + ∫ (dv/(v²+a²))
- B. A simple logarithmic integral
- C. Only a tan⁻¹ integral
- D. Impossible to evaluate
Answer: A. An integral of form ∫ (du/u) + ∫ (dv/(v²+a²))
The numerator 3x+5 can be split: (3/2)(2x+4) + (-1). The first part gives a logarithmic integral, the second gives a tan⁻¹ integral after completing the square.
The numerator 3x+5 can be split: (3/2)(2x+4) + (-1). The first part gives a logarithmic integral, the second gives a tan⁻¹ integral after completing the square.