Evaluate the following integrals using the definition of definite integral as the limit of a sum :
`int_(a)^(b)x^(3)dx`

Evaluate the following integrals using the definition of definite integral as the limit of a sum : int_(a)^(b)x^(m)dx[mne-1]

Evaluate the following integrals using the definition of definite integral as the limit of a sum : int_(a)^(b)e^(kx)dx (k = constant)

Evaluate the following integrals using the definition of definite integral as the limit of a sum : int_(a)^(b)sinxdx

Evaluate the following integrals using the definition of definite integral as the limit of a sum : int_(0)^(1)2^(x)dx

Evaluate the following integrals using the definition of definite integral as the limit of a sum : int_(1)^(3)(2x^(2)+5)dx

Evaluate the following integrals using the definition of a definite integral as the limit of a sum. int_(0)^(1) e^(x) dx