Question

Write the limit as a definite integral on the interval [a, b], where ci is any point in the ith subinterval.

Answer 1

Explanation

We have the following integral in the discrete sum form:

$\lim_{||\Delta||\to0}\sum_{i\mathop{=}1}^{\infty}(6c_i+3)\Delta x_i.$

In the interval [-9, 6].

To convert to the integral form, we convert each element of the discrete sum form:

$\begin{gathered} \lim_{||\Delta||\to0}\sum_{i\mathop{=}1}^{\infty}\rightarrow\int_{-9}^6 \\ 6c_i+3\rightarrow6x+3 \\ \Delta x_i\rightarrow dx \end{gathered}$

Replacing these in the formula above, we get the integral form:

$\int_{-9}^6(6x+3)\cdot dx.$Answer