Let I- - -4 - -3 sin x x dx- Then-

The correct option is C √( 3 ) 8 ≤ I≤√( 2 ) 6 I=∫^π3_π4sinxxdx sinxx is a decreasing function in given intervaldifference of limits =π3 π4 ...

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Byju's Answer

Standard XII

Mathematics

Integration by Substitution

Let I=∫ π /...

Question

Let $I = \int_{π / 4}^{π / 3} \frac{sin x}{x} d x$ . Then?

\frac{1}{2} \leq I \leq 1

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4 \leq I \leq 2 \sqrt{30}

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\frac{\sqrt{3}}{8} \leq I \leq \frac{\sqrt{2}}{6}

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1 \leq I \leq \frac{2 \sqrt{3}}{\sqrt{2}}

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Solution

The correct option is C $\frac{\sqrt{3}}{8} \leq I \leq \frac{\sqrt{2}}{6}$
$I = \int_{\frac{π}{4}}^{\frac{π}{3}} \frac{s i n x}{x} d x$
$\frac{s i n x}{x}$ is a decreasing function in given interval
difference of limits $= \frac{π}{3} - \frac{π}{4} = \frac{π}{12}$
so, $\frac{π}{12} \cdot \frac{s i n \frac{π}{3}}{\frac{π}{3}} \leq I \leq \frac{π}{12} \cdot \frac{s i n \frac{π}{4}}{\frac{π}{4}}$
$\frac{\sqrt{3}}{8} \leq I \leq \frac{\sqrt{2}}{6}$

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Similar questions

Q. Let

I = π / 3 \int π / 4 \frac{sin x}{x} d x

. Then

{[\frac{- 1 + i \sqrt{3}}{2}]}^{6} + {[\frac{- 1 - i \sqrt{3}}{2}]}^{6} + {[\frac{- 1 + i \sqrt{3}}{2}]}^{5} + {[\frac{- 1 - i \sqrt{3}}{2}]}^{5} =

{[\frac{- 1 + i \sqrt{3}}{2}]}^{6} + {[\frac{- 1 - i \sqrt{3}}{2}]}^{6} + {[\frac{- 1 + i \sqrt{3}}{2}]}^{5} + {[\frac{- 1 - i \sqrt{3}}{2}]}^{5} =

Let $I_{1} = {(\frac{π}{4})}^{2} + \sqrt{2}, I_{2} = {(t a n^{- 1} (\frac{1}{e}))}^{2} + \frac{2 e}{\sqrt{e^{2} + 1}}, I_{3} = (t a n^{- 1} e)^{2} + \frac{2}{\sqrt{e^{2} + 1}}$ , then which of the following is true?

Q. Express the following complex numbers in the standard form a + i b:
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(1 + i) (1 + 2 i)

(ii)

\frac{3 + 2 i}{- 2 + i}

(iii)

\frac{1}{(2 + i)^{2}}

(iv)

\frac{1 - i}{1 + i}

(v)

\frac{(2 + i)^{3}}{2 + 3 i}

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\frac{(1 + i) (1 + \sqrt{3} i)}{1 - i}

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(viii)

\frac{(1 - i)^{3}}{1 - i^{3}}

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\frac{5 + \sqrt{2} i}{1 - 2 \sqrt{i}}

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Let I=∫π/3π/4sinxxdx. Then?

The correct option is C √38≤I≤√26I=∫π3π4sinxxdxsinxx is a decreasing function in given intervaldifference of limits =π3−π4=π12so, π12⋅sinπ3π3≤I≤π12⋅sinπ4π4√38≤I≤√26

Let $I = \int_{π / 4}^{π / 3} \frac{sin x}{x} d x$ . Then?