Question

1)Express the given integral as the limit of a Riemann sum but do not evaluate: Attached

2) Use the Fundamental Theorem to evaluate the integral : Attached

Answer 1

Here is the integral for both questions : http://prntscr.com/9y8a1u

Answer 2

\[\int\limits_a^b f(x) dx=\lim_{n \rightarrow \infty} \sum_{i=1}^{n} f(a+i \Delta x) \cdot \Delta x \\ \text{ where } \Delta x =\frac{b-a}{n}\]

Answer 3

it should be easy to identify a and b and just plug them into the right hand side of the equation

Answer 4

and then identify f and plug in a+i(b-a)/n into that

Answer 5

you power rule for antiderivatives for number 4:
\[\int\limits x^{n} dx=\frac{x^{n+1}}{n+1}+C\]

Answer 6

where n can be anything but -1

Answer 7

Thank you @freckles! For the second question, am I supposed to use the power rule and then find the anti derivative?

Answer 8

yes