The correct option is B x^44+2x+C I=∫( x ^ 3 +2 ) dx =∫ x ^ 3 dx +2∫ dx I= x ^ 4 4 +2x+C #160; #160; #160; #160; .... {∵∫ x ...

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Integration of Piecewise Continuous Functions

Evaluate: ∫...

Question

Evaluate: $\int (x^{3} + 2) d x$

\frac{x^{4}}{4} + 2 x + C

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\frac{x^{4}}{5} + 2 x + C

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\frac{x^{4}}{4} + 4 x + C

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All of the above

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Solution

The correct option is B $\frac{x^{4}}{4} + 2 x + C$
$I = \int (x^{3} + 2) d x = \int x^{3} d x + 2 \int d x$
$I = \frac{x^{4}}{4} + 2 x + C$ .... ${∵ \int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C}$

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