f x - left begin matrix x - 2 for 0 Veq x leq 1 1 Isqrt x for 1 1leq xlleq 2A- 1-34 -2-1B- 1-32 -2-1C- 1-23 -2-1D- 1-34 -2-1

The correct option is A ( 1/3 )(4√(2) 1)∫_0^2 f(x) dx=∫_0^1f(x)dx+∫_1^2f(x)dx =1/3+2/3(2√(2) 1)= ( 1/3 )(4√(2) 1) ...

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Byju's Answer

Standard XII

Mathematics

Improper Integrals

f x =⟨ left b...

Question

$f (x) = {\begin{matrix} x^{2} f o r 0 \leq x \leq 1 \sqrt{x} f o r 1 \leq x \leq 2 \end{matrix} t h e n \int_{0}^{2} f (x) x d x =$

(\frac{1}{3}) (4 \sqrt{2} + 1)

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(\frac{1}{3}) (4 \sqrt{2} - 1)

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(\frac{1}{3}) (2 \sqrt{2} - 1)

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(\frac{1}{2}) (3 \sqrt{2} - 1)

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Solution

The correct option is B $(\frac{1}{3}) (4 \sqrt{2} - 1)$
$\int_{0}^{2} f (x) d x = \int_{0}^{1} f (x) d x + \int_{1}^{2} f (x) d x$
$= \frac{1}{3} + \frac{2}{3} (2 \sqrt{2} - 1) = (\frac{1}{3}) (4 \sqrt{2} - 1)$

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Similar questions

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Then find the value(s) of x for which f(x)=2.

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Then find the value(s) of x for which f(x)=2.

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f(x)={x2 for 0≤x≤1√x for 1≤x≤2 then∫20f(x)x dx=

The correct option is B (13)(4√2−1)∫20f(x) dx=∫10f(x)dx+∫21f(x)dx =13+23(2√2−1)=(13)(4√2−1)

$f (x) = {\begin{matrix} x^{2} f o r 0 \leq x \leq 1 \sqrt{x} f o r 1 \leq x \leq 2 \end{matrix} t h e n \int_{0}^{2} f (x) x d x =$

The correct option is B $(\frac{1}{3}) (4 \sqrt{2} - 1)$
$\int_{0}^{2} f (x) d x = \int_{0}^{1} f (x) d x + \int_{1}^{2} f (x) d x$
$= \frac{1}{3} + \frac{2}{3} (2 \sqrt{2} - 1) = (\frac{1}{3}) (4 \sqrt{2} - 1)$