Skip to content
We use only essential cookies to keep you signed in and remember your preferences. See our Cookie Policy.
TestStop
MocksPracticeResourcesIndiaBlogPricing
Sign in
Questions › DSE › DSE 2011 › Q21
2 marksMathematics › Integration and its applications › Indefinite and definite integralsModerateabout 3 min

DSE 2011 Question 21: Integration and its applications

Suppose the function f:ℜ++→ℜf:\Re_{++}\to\Ref:ℜ++​→ℜ is given by f(x)=∫1xt−1 dtf(x)=\int_{1}^{x}t^{-1}\,dtf(x)=∫1x​t−1dt. Consider the following statements: for x,y∈ℜ++x,y\in\Re_{++}x,y∈ℜ++​: (i) f(x+y)=f(x)+f(y)f(x+y)=f(x)+f(y)f(x+y)=f(x)+f(y); (ii) f(xy)=f(x)+f(y)f(xy)=f(x)+f(y)f(xy)=f(x)+f(y). In general,

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Plain-text version

Suppose the function f:ℜ₊₊→ℜ is given by f(x)=∫₁^xt⁻¹ dt. Consider the following statements: for x,y∈ℜ₊₊: (i) f(x+y)=f(x)+f(y); (ii) f(xy)=f(x)+f(y). In general, (A) (i) is true and (ii) is false. (B) (i) is false and (ii) is true. (C) Both are true. (D) Both are false.

Also written as: Suppose the function f: Re_(++)-> Re is given by f(x)= integral_1^xt^(-1) dt. Consider the following statements: for x,y in Re_(++): (i) f(x+y)=f(x)+f(y); (ii) f(xy)=f(x)+f(y). In general,

Integration and its applications has come up 43 times in 6 exams since 2007.

What this question tests

This question is on Indefinite and definite integrals, part of Integration and its applications in Mathematics.

Antiderivatives and areas under curves for standard functions.

TestStop has 21 past-paper questions on this subtopic.

Practise Integration and its applicationsMore on Indefinite and definite integrals

Similar questions from other papers

  • IIT JAM 2026 · Q10The area under the curve f(x)=x⁵ e^(x³) between x=1 and x=2 is
  • UGC-NET 2025 · Q5Assume that the rate of investment is described by the function I(t) = 12 t^(1/3) and capital stock k(0) = 25. Find the time path of capital stock k.
  • IIT JAM 2024 · Q46Let the inverse demand function be p = e^(-x/2), where x is quantity and p is price. Then, at p = 0.5, the consumer surplus is equal to (rounded off to two decimal…
  • CUET-PG 2023 Shift 1 · Q92∫ ((e^(8ln x) - e^(4ln x))/(e^(4ln x) - e^(2ln x))) dx 1. (e^(8x) - e^(4x))/(e^(4x) - e^(2x)) + C 2. x⁵/5 + x³/3 + C 3. x⁵/5 - x³/3 + C 4.
  • IIT JAM 2023 · Q47Let E be the area of the region bounded by y=x² and y=8√x, x≥0. Then 30E is equal to (round off to 1 decimal place).

Question from the DSE 2011 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.