Integral of -x3-1-x2-2 The limits are from x-0 to x-2

∫ _ 0 ^ 2 √( x ^ 3 ) #160; +1+√( x ^ 2 ) +2 dx =∫ _ 0 ^ 2 ( x ^ 3 / 2 + x ^ 2 / 3 +3 ) #160; dx = 2 5 [ x ^ 5 / 2 ] #160; _ 0 ^ 2 + ...

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De-Moivre's Theorem

Integral of ...

Question

Integral of $((\sqrt{x^{3}}) + 1) + ((\sqrt[3]{x^{2}}) + 2)$ The limits are from $x = 0$ to $x = 2$

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The following expansion can be used to find the difficult limits easily. We recommend you to remember them.

$1) e^{x} = \frac{x}{1!} + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + . . . . . .$

$2) l n (1 + x) = x - \frac{x^{2}}{2} + \frac{x^{3}}{3} . . . . .,$ -1 < x $\geq$ 1

$3) s i n x = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \frac{x^{7}}{7!} . . . . .$

$4) c o s x = 1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!} - \frac{x^{6}}{6!} . . . . . .$

$5) t a n x = x + \frac{x^{3}}{3!} + \frac{2 x^{5}}{15!} . . . . . .$

$6) a^{x} = 1 + (l n a) x + (l n a)^{2} \frac{x^{2}}{2!} . . . . . . .$

We will be using these expansions to solve problems in this topic.

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ln x^{2}, 2 ln x; x > 0

\frac{x^{2}}{x}, x

∣ x ∣^{2}, x^{2}

∣ x ∣^{3}, x^{3}

x

\frac{({sin}^{- 1} x)^{3 / 2}}{\sqrt{1 - x^{2}}}

\frac{x^{2} - x}{x^{3} - x^{2} + x - 1}

x

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