A Calculus problem #2 ( ⊙ v ⊙ ≀ ) ^ \widehat{\dbinom{\odot_\text{v}\odot}{\wr}}

Level 1

If F ( x ) = ∫ 0 x 2 sin ⁡ ( t ) d t F(x)= \displaystyle \int_0^{x^2}\sin(t)\ dt , find F ′ ( x ) F'(x) .

2 x ( x 2 ) 2x(x^{2}) 2 x cos ⁡ ( x 2 ) 2x \cos(x^{2}) 3 x 2 3x^{2} 2 x sin ⁡ ( x 2 ) 2x \sin(x^{2})

Fred Looka by Fred Looka , 21, Japan

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1 solution

F ( x ) = ∫ 0 x 2 sin ⁡ t d t = 1 − cos ⁡ ( x 2 ) F ′ ( x ) = d d x ( 1 − cos ⁡ ( x 2 ) ) = 2 x sin ⁡ ( x 2 ) \begin{aligned} F(x) & = \int_0^{x^2} \sin t \ dt = 1 - \cos (x^2) \\ F'(x) & = \frac d{dx} \left(1 - \cos (x^2)\right) = \boxed{2x \sin (x^2)} \end{aligned}

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DYLAN MARSHALL - 3 years, 3 months ago

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????????????

Chew-Seong Cheong - 3 years, 3 months ago

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exactly, i might not understand calculus, only that it was developed by Gottfried Leibniz

DYLAN MARSHALL - 3 years, 2 months ago

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