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Questions › DSE › DSE 2020 › Q47
4 marks, −1Mathematics › Integration and its applications › Integration techniquesModerateabout 3 min

DSE 2020 Question 47: Integration and its applications

Consider a decreasing differentiable function g:R+→R+g:\mathbb{R}_+\to\mathbb{R}_+g:R+​→R+​ and an increasing continuous function f:R+→R+f:\mathbb{R}_+\to\mathbb{R}_+f:R+​→R+​. If F:R+→R+F:\mathbb{R}_+\to\mathbb{R}_+F:R+​→R+​ satisfies F(x)=∫0g(x)f(t) dtF(x)=\int_0^{g(x)}f(t)\,dtF(x)=∫0g(x)​f(t)dt for every x∈R+x\in\mathbb{R}_+x∈R+​, then FFF is

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Consider a decreasing differentiable function g:ℝ₊→ℝ₊ and an increasing continuous function f:ℝ₊→ℝ₊. If F:ℝ₊→ℝ₊ satisfies F(x)=∫₀^(g(x))f(t) dt for every x∈ℝ₊, then F is (A) Increasing over [0,a] and decreasing over [a,∞), for some a>0 (B) Decreasing over [0,a] and increasing over [a,∞), for some a>0 (C) Increasing (D) Decreasing

Also written as: Consider a decreasing differentiable function g:R_+->R_+ and an increasing continuous function f:R_+->R_+. If F:R_+->R_+ satisfies F(x)= integral_0^(g(x))f(t) dt for every x in R_+, then F is

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

What this question tests

This question is on Integration techniques, part of Integration and its applications in Mathematics.

Substitution, integration by parts, partial fractions and improper integrals.

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