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Calculus Level 3

$\large\frac{d}{dx}\left(\int_{x^{2}}^{3} (\arccos(t)-2) \, dt\right) =\, ?$

3x( 2 +\arccos(x^{2}))

2x( 2- \arccos(x^{2}))

2x( 2+ \arccos(x^{2}))

2x( 3 - \arccos(x^{2}))

1 solution

Hana Wehbi
Jun 16, 2016

$\large\frac{d}{dx}\left(\int_{x^{2}}^{3} (\arccos(t)-2)dt\right)$

= $\large\frac{d}{dx}[-\int_{3}^{x^2}(arccos(t)-2)dt]$

= $\large(-1)\frac{d}{dx}[\int_{3}^{x^{2}}(arccos(t)-2)dt]$

= $\large(-2x)[(arccos(x^{2})-2)]$