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Using the fact that $0 \leq f (x) \leq g (x), c < x < d$
$\Rightarrow \int_{c}^{d} f (x) d x \leq \int_{c}^{d} g (x) d x$ we can conclude that
$\int_{1}^{3} \sqrt{3 + x^{3}}$ lies in the interval

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12,3

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32,5

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detailed solution

Correct option is D

For x∈(1,3),2<3+x3<30 so 2∫13 dx<∫13 3+x3dx<30∫13 dx⇒4<∫13 3+x3dx<230

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Using the fact that 0≤f(x)≤g(x),c<x<d ⇒∫cd f(x)dx≤∫cd g(x)dx we can conclude that ∫13 3+x3 lies in the interval

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Ready to Test Your Skills?

free study material

Using the fact that $0 \leq f (x) \leq g (x), c < x < d$
$\Rightarrow \int_{c}^{d} f (x) d x \leq \int_{c}^{d} g (x) d x$ we can conclude that
$\int_{1}^{3} \sqrt{3 + x^{3}}$ lies in the interval