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Evaluate the following integral: int0^(1...

Evaluate the following integral: `int_0^(15)[x^2]dx`

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Given:`int_0^(15)[x^2]dx`
`I=int_0^(15)[x^2]dx`
Now as `n<=[n] Then `int_a^b f(x)dx=int_a^c f(x)dx+int_c^b f(x)dx`
`I=int_0^1[x^2]dx+int_1^2 [x^2]dx+int_2^3 [x^2]dx+........+int_(14)^(15)[x^2]dx`
`I=0+1+2+3+4+5+6+......+14`
As sum of n terms =`(n(n+1))/2`
`I=(14(14+1))/2`
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