definite integration - properties

1.\int_{0}^{x}[1+t]^{3}dt

2.\int_{0}^{x}[x]dx

plz help sir

2 Answers

1357
Manish Shankar ·

2.\int_{0}^{x}[x]dx=\int_{0}^{[x]}[x]dx+\int_{[x]}^{x}[x]dx=\int_{0}^{1}0dx+\int_{1}^{2}1dx+...+\int_{[x-1]}^{[x]}[x-1]dx+\int_{[x]}^{x}[x]dx=0+1+2+3+...[x-1]+[x](x-[x])

1357
Manish Shankar ·

similarly you can try the first one

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