G.$$I=$$∫$$01$$ $$0dx+$$∫$$12$$ $$1dx+$$∫$$23$$ $$2dx+$$∫$$34$$ $$3dx+$$∫$$45$$ $$4dx=0+(x)12+2(x)23+3(x)34+4(x)45=1+2(1)+3(1)+4(1)=10$$

Evaluation of definite integrals

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$\int_{0}^{5} [x] d x =$

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Solution

$\begin{array}{l} G . I = \int_{0}^{1} 0 d x + \int_{1}^{2} 1 d x + \int_{2}^{3} 2 d x + \int_{3}^{4} 3 d x + \int_{4}^{5} 4 d x \\ = 0 + (x)_{1}^{2} + 2 (x)_{2}^{3} + 3 (x)_{3}^{4} + 4 (x)_{4}^{5} \\ = 1 + 2 (1) + 3 (1) + 4 (1) = 10 \end{array}$

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