The correct option is B 26 ∫_0^4[2x+3]dx=∫_0^4([2x]+3)dx =∫_0^4[2x]dt+∫_0^43 nbsp; dx ∫_0^π/20 nbsp; dx+∫_1/2^11 nbsp; dx nbsp; + nbsp; ...

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Exponential Representation for Irrational Numbers

∫04[2x+3]dx=

Question

$\int_{0}^{4} [2 x + 3] d x =$

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Solution

The correct option is B 26
$\int_{0}^{4} [2 x + 3] d x = \int_{0}^{4} ([2 x] + 3) d x$
$= \int_{0}^{4} [2 x] d t + \int_{0}^{4} 3 d x$
$\int_{0}^{\frac{π}{2}} 0 d x + \int_{\frac{1}{2}}^{1} 1 d x + \int_{1}^{\frac{1}{3}} 2 d x + \int_{1 \frac{1}{2}}^{2} 3 d x + \int_{2}^{2 \frac{1}{2}} 4 d x + \int_{2 \frac{1}{2}}^{3} 5 d x + \int_{3}^{3 \frac{1}{2}} 6 d x + \int_{3 \frac{1}{2}}^{4} 7 d x + 3 (4)$
$\frac{1}{2} (0 + 1 + 2 + . . . . .7) + 12$
$= 14 + 12$
$= 26$

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