If f x -2xsin x cos t3 dt - then f-x is equal to -

The correct option is A cos ( sin^3 x) cos x 1 cos ( 8x^3) Given, f(x) = #160;∫_2x^sin xcos t^3 dt Using Leibnitz's rule, we get f'(x) = cos ( ...

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Standard XII

Mathematics

Definite Integral as Limit of Sum

If f x =∫2x...

Question

If $f (x) = \int_{2 x}^{sin x} cos (t^{3}) d t,$ then $f^{'} (x)$ is equal to :

cos ({sin}^{3} x) cos x - 1 cos (8 x^{3})

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sin ({sin}^{3} x) sin x - 2 sin (8 x^{3})

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cos ({cos}^{3} x) cos x - 2 cos (8 x^{3})

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cos ({sin}^{3} x) - cos (8 x^{3})

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sin ({sin}^{3} x) cos x - 2 sin (8 x^{3})

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Solution

The correct option is A $cos ({sin}^{3} x) cos x - 1 cos (8 x^{3})$
Given, $f (x) = \int_{2 x}^{sin x} cos t^{3} d t$
Using Leibnitz's rule, we get
$f^{'} (x) = cos ({sin}^{3} x) \frac{d}{d x} (sin x) - cos (2 x)^{3} \frac{d}{d x} (2 x)$
$= cos ({sin}^{3} x) - cos 8 x^{3} (2)$

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If f(x)=∫sinx2xcos(t3)dt, then f′(x) is equal to :

The correct option is A cos(sin3x)cosx−1cos(8x3)Given, f(x)=∫sinx2xcost3dtUsing Leibnitz's rule, we getf′(x)=cos(sin3x)ddx(sinx)−cos(2x)3ddx(2x) =cos(sin3x)−cos8x3(2)

If $f (x) = \int_{2 x}^{sin x} cos (t^{3}) d t,$ then $f^{'} (x)$ is equal to :

The correct option is A $cos ({sin}^{3} x) cos x - 1 cos (8 x^{3})$
Given, $f (x) = \int_{2 x}^{sin x} cos t^{3} d t$
Using Leibnitz's rule, we get
$f^{'} (x) = cos ({sin}^{3} x) \frac{d}{d x} (sin x) - cos (2 x)^{3} \frac{d}{d x} (2 x)$
$= cos ({sin}^{3} x) - cos 8 x^{3} (2)$